In this notebook we search for surgery diagrams of the branching sets of quotients of symmetric fillings of asymmetric L-space knots in A.

This is the complete list of the 49 hyperbolic symmetric slopes on knots in A.

In [1]:
symmetric_slopes=[['t12533', (-3, 1)],
 ['t12533', (-2, 1)],
 ['t12533', (-1, 1)],
 ['t12533', (0, 1)],
 ['t12533', (1, 1)],
 ['t12533', (-1, 2)],
 ['t12681', (-1, 1)],
 ['t12681', (1, 1)],
 ['t12681', (-1, 2)],
 ['t12681', (-2, 3)],
 ['t12681', (-1, 3)],
 ['o9_38928', (-2, 1)],
 ['o9_38928', (-1, 1)],
 ['o9_38928', (0, 1)],
 ['o9_38928', (1, 1)],
 ['o9_38928', (2, 1)],
 ['o9_39162', (-1, 1)],
 ['o9_39162', (1, 1)],
 ['o9_39162', (2, 1)],
 ['o9_39162', (1, 2)],
 ['o9_39162', (1, 4)],
 ['o9_40363', (-1, 1)],
 ['o9_40363', (1, 1)],
 ['o9_40363', (-1, 2)],
 ['o9_40363', (-1, 3)],
 ['o9_40363', (-3, 4)],
 ['o9_40487', (-2, 1)],
 ['o9_40487', (-1, 1)],
 ['o9_40487', (0, 1)],
 ['o9_40487', (1, 1)],
 ['o9_40487', (2, 1)],
 ['o9_40487', (3, 1)],
 ['o9_40487', (1, 2)],
 ['o9_40504', (-2, 1)],
 ['o9_40504', (-1, 1)],
 ['o9_40504', (0, 1)],
 ['o9_40504', (1, 1)],
 ['o9_40504', (2, 1)],
 ['o9_40582', (-1, 1)],
 ['o9_40582', (0, 1)],
 ['o9_40582', (1, 1)],
 ['o9_40582', (2, 1)],
 ['o9_40582', (4, 1)],
 ['o9_40582', (1, 2)],
 ['o9_42675', (-2, 1)],
 ['o9_42675', (-1, 1)],
 ['o9_42675', (0, 1)],
 ['o9_42675', (1, 1)],
 ['o9_42675', (2, 1)]]

We also need the list of slopes which have 3 different quotients. For those we want to find three different branching sets.

In [2]:
more_symmetries=[['t12681', (1, 1)], ['o9_38928', (2, 1)], ['o9_40363', (1, 1)], ['o9_40504', (2, 1)], ['o9_42675', (-2, 1)]]

In a first step we search for branching sets in the 3-sphere by going to the HT link table.

In [3]:
import time
import snappy
import pandas
DBChomologies = pandas.read_csv("DBChomologies_non_alternating.csv") # We load a list of all non alternating links in the HTLinkExteriors together with their homologies (if the homology is cyclic) and their crossing numbers.
### REMARK: To build the list we need to run the code in the file Build_DBChomologies which takes around 60 minutes. Here we just load it.


def double_branched_cover(link):
    """
    Returns the double branched cover of the link.
    """
    L=link.copy()
    for i in range(L.num_cusps()):
        L.dehn_fill((2,0),i)
    for cov in L.covers(2):
        if (2.0, 0.0) not in cov.cusp_info('filling'):
            return cov

def better_is_isometric_to(X,Y,index):
    """
    Returns True if X and Y are isometric.
    Returns False if X and Y have different homologies. TO DO: Use volume to rigorously distinguish X and Y.
    Returns 'unclear' if SnapPy cannot verify it.
    The higher the index the harder SnapPy tries.
    """     
    w='unclear'
    if X.homology()!=Y.homology():
        w=False
    if w=='unclear':
        for i in (0,index):
            try:
                w=X.is_isometric_to(Y)
            except RuntimeError:
                pass
            except snappy.SnapPeaFatalError:
                pass
            if w==True:
                break
            if w==False:
                w='unclear'
            X.randomize()
            Y.randomize()
            i=i+1
    return w

def possible_DBC(homologies,max_crossings=15):
    """
    Takes a list of orders of homologies and returns a list consisting of all DBC of alternating links in the HT link table with that homologies together with the link names.
    """
    DBCList=[]
    LINKS=[]
    for order in homologies:
        LINKS=LINKS+DBChomologies.loc[(DBChomologies['homology']==order) & (DBChomologies['crossings']<=max_crossings)]['knot'].tolist()
    for link in LINKS:
        L=snappy.Manifold(link)
        D=double_branched_cover(L)
        DBCList.append([D,link])
    return DBCList

### The following two functions are written by Dunfield and search for positive triangulations.

def all_positive(manifold):
    return manifold.solution_type() == 'all tetrahedra positively oriented'

def find_positive_triangulation(manifold, tries=100):
    M = manifold.copy()
    for i in range(tries):
        if all_positive(M):
            return M
        M.randomize()
    for d in M.dual_curves():
        X = M.drill(d)
        X = X.filled_triangulation()
        X.dehn_fill((1,0))
        for i in range(tries):
            if all_positive(X):
                return X
            X.randomize()

    # In the closed case, here is another trick.
    if all(not c for c in M.cusp_info('is_complete')):
        for i in range(tries):
            # Drills out a random edge
            X = M.__class__(M.filled_triangulation())
            if all_positive(X):
                return X
            M.randomize()
            
def better_find_positive_triangulation(M,tries=1):
    '''
    Search for a positive triangulation, but ignores errors.
    '''
    RandomizeCount=0
    while RandomizeCount<tries:
        try:
            X=find_positive_triangulation(M)
            return X
        except snappy.SnapPeaFatalError:
            M.randomize()
            RandomizeCount=RandomizeCount+1
    return None

def is_alternating(knot,slope,try_hard=False,index=10,tries=1,max_cro=15):
    '''
    Checks if the slope is alternating.
    '''
    K=snappy.Manifold(knot)
    K.dehn_fill(slope)
    DBC=possible_DBC([K.homology().order()],max_crossings=max_cro) 
    for D in DBC:
        w=better_is_isometric_to(D[0],K,index)
        if w==True:
            return [slope,D[1]]
    if try_hard:
        X=better_find_positive_triangulation(K,tries)
        if X is not None:
            for D in DBC:
                Y=better_find_positive_triangulation(D[0],tries)
                if Y is not None:
                    w=better_is_isometric_to(X,Y,index)
                    if w==True:
                        return [slope,D[1]]
    return False
In [4]:
start_time = time.time()
branching_sets=[]
for (knot,slope) in symmetric_slopes:
    w=is_alternating(knot,slope,index=25,max_cro=13)
    if w!=False:
        branching_sets.append([knot,w[0],w[1]])
        print('We found a branching set:',knot,slope,w[1])
        
print('Total number of branching sets we have found:', len(branching_sets))
print('Total time taken: %s minutes ---' % ((time.time() - start_time)/60))

We found a branching set: t12533 (-1, 1) L12n789
We found a branching set: t12533 (0, 1) K12n407
We found a branching set: t12681 (-1, 1) L11n172
We found a branching set: o9_38928 (0, 1) L11n178
We found a branching set: o9_38928 (1, 1) K11n172
We found a branching set: o9_39162 (1, 1) L12n1050
We found a branching set: o9_40363 (-1, 1) L12n785
We found a branching set: o9_40487 (0, 1) L11n152
We found a branching set: o9_40487 (1, 1) K11n147
We found a branching set: o9_40504 (0, 1) L11n179
We found a branching set: o9_40504 (1, 1) K11n166
We found a branching set: o9_40582 (0, 1) L13n4413
We found a branching set: o9_40582 (1, 1) K13n2958
We found a branching set: o9_42675 (-1, 1) K12n730
We found a branching set: o9_42675 (0, 1) L12n702
Total number of branching sets we have found: 15
Total time taken: 1.4020240227381389 minutes ---

We get 15 branchings sets in the 3-sphere. It will turn out that together with the Seifert fibered alternating 3-sphere quotients these is the complete list of branching sets in the 3-sphere.

In [5]:
branching_sets
Out[5]:
[['t12533', (-1, 1), 'L12n789'],
 ['t12533', (0, 1), 'K12n407'],
 ['t12681', (-1, 1), 'L11n172'],
 ['o9_38928', (0, 1), 'L11n178'],
 ['o9_38928', (1, 1), 'K11n172'],
 ['o9_39162', (1, 1), 'L12n1050'],
 ['o9_40363', (-1, 1), 'L12n785'],
 ['o9_40487', (0, 1), 'L11n152'],
 ['o9_40487', (1, 1), 'K11n147'],
 ['o9_40504', (0, 1), 'L11n179'],
 ['o9_40504', (1, 1), 'K11n166'],
 ['o9_40582', (0, 1), 'L13n4413'],
 ['o9_40582', (1, 1), 'K13n2958'],
 ['o9_42675', (-1, 1), 'K12n730'],
 ['o9_42675', (0, 1), 'L12n702']]
In [6]:
symmetric_slopes=[x for x in symmetric_slopes if x not in [[y[0],y[1]] for y in branching_sets]]
In [7]:
len(symmetric_slopes)
Out[7]:
34
In [8]:
symmetric_slopes
Out[8]:
[['t12533', (-3, 1)],
 ['t12533', (-2, 1)],
 ['t12533', (1, 1)],
 ['t12533', (-1, 2)],
 ['t12681', (1, 1)],
 ['t12681', (-1, 2)],
 ['t12681', (-2, 3)],
 ['t12681', (-1, 3)],
 ['o9_38928', (-2, 1)],
 ['o9_38928', (-1, 1)],
 ['o9_38928', (2, 1)],
 ['o9_39162', (-1, 1)],
 ['o9_39162', (2, 1)],
 ['o9_39162', (1, 2)],
 ['o9_39162', (1, 4)],
 ['o9_40363', (1, 1)],
 ['o9_40363', (-1, 2)],
 ['o9_40363', (-1, 3)],
 ['o9_40363', (-3, 4)],
 ['o9_40487', (-2, 1)],
 ['o9_40487', (-1, 1)],
 ['o9_40487', (2, 1)],
 ['o9_40487', (3, 1)],
 ['o9_40487', (1, 2)],
 ['o9_40504', (-2, 1)],
 ['o9_40504', (-1, 1)],
 ['o9_40504', (2, 1)],
 ['o9_40582', (-1, 1)],
 ['o9_40582', (2, 1)],
 ['o9_40582', (4, 1)],
 ['o9_40582', (1, 2)],
 ['o9_42675', (-2, 1)],
 ['o9_42675', (1, 1)],
 ['o9_42675', (2, 1)]]

Next we will search for branching sets in more general manifolds. For that we will take links in the HT link tables fill some one component of it to get a surgery diagram of a link in a manifold. Then we take the double branched cover of that link and search for a match with a symmetric filling on A.

In [9]:
DBChomologies_branching = pandas.read_csv("DBChomologies_one_filling.csv")  
### REMARK: To build the list we need to run the code in the file Build_DBChomologies which takes around 3 days. Here we just load it.


def double_branched_cover(link):
    """
    Returns the double branched covers of the link. This works also for links in a more general manifold. 
    Note that a knot in a more general manifold may have more than one double branched cover 
    (or no double branched cover at all if the knot represents a primitive element in homology).
    This function will return the complete list of all double branched covers of the link.
    """
    L=link.copy()
    for i in range(L.num_cusps()):
        if L.cusp_info(i).filling==(0.0, 0.0):
            L.dehn_fill((2,0),i)
    return [cov for cov in L.covers(2) if (2.0, 0.0) not in cov.cusp_info('filling')]

def possible_DBC_surgery_diagrams(homologies,max_crossings=15):
    """
    Reads off the possible surgery diagrams.
    """
    DBCList=[]
    LINKS=[]
    CUSPS=[]
    SLOPES_STRINGS=[]
    for order in homologies:
        LINKS=LINKS+DBChomologies_branching.loc[(DBChomologies_branching['homology']==order) & (DBChomologies_branching['crossings']<=max_crossings)]['knot'].tolist()
        CUSPS=CUSPS+DBChomologies_branching.loc[(DBChomologies_branching['homology']==order) & (DBChomologies_branching['crossings']<=max_crossings)]['cusp'].tolist()
        SLOPES_STRINGS=SLOPES_STRINGS+DBChomologies_branching.loc[(DBChomologies_branching['homology']==order) & (DBChomologies_branching['crossings']<=max_crossings)]['filling'].tolist()
    SLOPES=[]
    for string in SLOPES_STRINGS:
        string_without_brackets=string[1:-1]
        SLOPES.append(tuple(map(int, string_without_brackets.split(', '))))
    for i in range(0,len(LINKS)):
        DBCList.append([LINKS[i],SLOPES[i],CUSPS[i]])
    return DBCList

def search_for_branching_set(knot,slope,try_hard=False,index=10,tries=1,max_crossings=15):
    '''
    Searchs for a surgery diagram of the rbanching set
    '''  
    K=snappy.Manifold(knot)
    K.dehn_fill(slope)
    DBC=possible_DBC_surgery_diagrams([K.homology().order()],max_crossings) 
    for DIAGRAM in DBC:
        L=snappy.Manifold(DIAGRAM[0])
        L.dehn_fill(DIAGRAM[1],DIAGRAM[2])
        for D in double_branched_cover(L):
            w=better_is_isometric_to(D,K,index)
            if w==True:
                return [[knot,slope,DIAGRAM[0],DIAGRAM[1],DIAGRAM[2]]]
    if try_hard:
        X=better_find_positive_triangulation(K,tries)
        if X is not None:
            for DIAGRAM in DBC:
                L=snappy.Manifold(DIAGRAM[0])
                L.dehn_fill(DIAGRAM[1],DIAGRAM[2])
                for D in double_branched_cover(L):
                    Y=better_find_positive_triangulation(D,tries)
                    if Y is not None:
                        w=better_is_isometric_to(X,Y,index)
                        if w==True:
                            return [[knot,slope,DIAGRAM[0],DIAGRAM[1],DIAGRAM[2]]]                                  
    return False

def search_for_three_branching_sets(knot,slope,try_hard=False,index=10,tries=1,max_crossings=15):
    '''
    Searchs for a surgery diagram of the branching set
    '''  
    BRANCHING_SETS=[]
    K=snappy.Manifold(knot)
    K.dehn_fill(slope)
    homologies=[]
    DBC=possible_DBC_surgery_diagrams([K.homology().order()],max_crossings) 
    for DIAGRAM in DBC:
        L=snappy.Manifold(DIAGRAM[0])
        L.dehn_fill(DIAGRAM[1],DIAGRAM[2])
        for D in double_branched_cover(L):
            w=better_is_isometric_to(D,K,index)
            if w==True:
                BRANCHING_SETS=BRANCHING_SETS+[[knot,slope,DIAGRAM[0],DIAGRAM[1],DIAGRAM[2]]]
                for i in range(L.num_cusps()):
                    if L.cusp_info(i).filling==(0.0, 0.0):
                        L.dehn_fill((1,0),i)
                if L.homology().order() not in homologies:
                    homologies.append(L.homology().order())
                if len(homologies)==3:
                    return BRANCHING_SETS
    if try_hard:
        X=better_find_positive_triangulation(K,tries)
        if X is not None:
            for DIAGRAM in DBC:
                L=snappy.Manifold(DIAGRAM[0])
                L.dehn_fill(DIAGRAM[1],DIAGRAM[2])
                for D in double_branched_cover(L):
                    Y=better_find_positive_triangulation(D,tries)
                    if Y is not None:
                        w=better_is_isometric_to(X,Y,index)
                        if w==True:
                            BRANCHING_SETS=BRANCHING_SETS+[[knot,slope,DIAGRAM[0],DIAGRAM[1],DIAGRAM[2]]]
                            for i in range(L.num_cusps()):
                                if L.cusp_info(i).filling==(0.0, 0.0):
                                    L.dehn_fill((1,0),i)
                            if L.homology().order() not in homologies:
                                homologies.append(L.homology().order())
                            if len(homologies)==3:
                                return BRANCHING_SETS
    return BRANCHING_SETS
In [10]:
start_time = time.time()
for (knot,slope) in symmetric_slopes:
    if [knot,slope] in more_symmetries:
        w=search_for_three_branching_sets(knot,slope,index=3,max_crossings=15)
        if w==[]:
            w=False
    else:
        w=search_for_branching_set(knot,slope,index=3,max_crossings=15)
    if w!=False:
        branching_sets=branching_sets+w
        print('We found a branching set:',w)
        
print('Total number of branching sets we have found:', len(branching_sets))
print('Total time taken: %s minutes ---' % ((time.time() - start_time)/60))

We found a branching set: [['t12533', (-3, 1), 'L11n350', (-4, 1), 1]]
We found a branching set: [['t12533', (-2, 1), 'L12n722', (3, 1), 0]]
We found a branching set: [['t12533', (1, 1), 'L13n7360', (2, 1), 1]]
We found a branching set: [['t12533', (-1, 2), 'L11n192', (-3, 1), 0]]
We found a branching set: [['t12681', (1, 1), 'L11n419', (5, 1), 1], ['t12681', (1, 1), 'L12n1907', (3, 1), 1], ['t12681', (1, 1), 'L13n7356', (2, 1), 1]]
We found a branching set: [['t12681', (-1, 2), 'L10a81', (3, 1), 0]]
We found a branching set: [['t12681', (-2, 3), 'L13n4363', (-5, 3), 0]]
We found a branching set: [['t12681', (-1, 3), 'L11a282', (-4, 1), 0]]
We found a branching set: [['o9_38928', (-2, 1), 'L12n1949', (2, 1), 1]]
We found a branching set: [['o9_38928', (-1, 1), 'L12n703', (3, 1), 0]]
We found a branching set: [['o9_38928', (2, 1), 'L10a105', (-2, 1), 0], ['o9_38928', (2, 1), 'L10a105', (-2, 1), 1], ['o9_38928', (2, 1), 'L10n54', (-8, 1), 0], ['o9_38928', (2, 1), 'L10n54', (-8, 1), 1], ['o9_38928', (2, 1), 'L13n7433', (-3, 1), 1]]
We found a branching set: [['o9_39162', (-1, 1), 'L13n9864', (-3, 1), 0]]
We found a branching set: [['o9_39162', (2, 1), 'L10n44', (7, 1), 0]]
We found a branching set: [['o9_39162', (1, 2), 'L12n784', (3, 1), 0]]
We found a branching set: [['o9_39162', (1, 4), 'L13n4343', (-7, 4), 0]]
We found a branching set: [['o9_40363', (1, 1), 'L11n419', (7, 1), 1], ['o9_40363', (1, 1), 'L13n9451', (3, 1), 1], ['o9_40363', (1, 1), 'L14n43377', (2, 1), 1]]
We found a branching set: [['o9_40363', (-1, 2), 'L11a225', (-3, 1), 0]]
We found a branching set: [['o9_40363', (-1, 3), 'L12a1861', (4, 1), 1]]
We found a branching set: [['o9_40363', (-3, 4), 'L13n4363', (-7, 4), 0]]
We found a branching set: [['o9_40487', (-2, 1), 'L12n1041', (-2, 1), 0]]
We found a branching set: [['o9_40487', (-1, 1), 'L12n722', (-3, 1), 0]]
We found a branching set: [['o9_40487', (2, 1), 'L11n333', (2, 1), 1]]
We found a branching set: [['o9_40487', (3, 1), 'L12n1314', (7, 1), 0]]
We found a branching set: [['o9_40487', (1, 2), 'L12n968', (-3, 1), 0]]
We found a branching set: [['o9_40504', (-2, 1), 'L12n1037', (-2, 1), 0]]
We found a branching set: [['o9_40504', (-1, 1), 'L12n715', (-3, 1), 0]]
We found a branching set: [['o9_40504', (2, 1), 'L10a146', (-2, 1), 1], ['o9_40504', (2, 1), 'L10a146', (-2, 1), 2], ['o9_40504', (2, 1), 'L13n7421', (-3, 1), 1], ['o9_40504', (2, 1), 'L13n8521', (5, 1), 1]]
We found a branching set: [['o9_40582', (-1, 1), 'L10n44', (-5, 3), 0]]
We found a branching set: [['o9_40582', (2, 1), 'L13n9833', (3, 1), 0]]
We found a branching set: [['o9_40582', (4, 1), 'L11n350', (-5, 1), 1]]
We found a branching set: [['o9_40582', (1, 2), 'L12n996', (3, 1), 0]]
We found a branching set: [['o9_42675', (-2, 1), 'L10n24', (6, 1), 1], ['o9_42675', (-2, 1), 'L11n223', (-2, 1), 0], ['o9_42675', (-2, 1), 'L13n5311', (2, 1), 0], ['o9_42675', (-2, 1), 'L13n9832', (8, 3), 1]]
We found a branching set: [['o9_42675', (1, 1), 'L14n24428', (5, 3), 0]]
We found a branching set: [['o9_42675', (2, 1), 'L13n7552', (-2, 1), 1]]
Total number of branching sets we have found: 63
Total time taken: 86.03129815657934 minutes ---
In [11]:
branching_sets.sort()
branching_sets
Out[11]:
[['o9_38928', (-2, 1), 'L12n1949', (2, 1), 1],
 ['o9_38928', (-1, 1), 'L12n703', (3, 1), 0],
 ['o9_38928', (0, 1), 'L11n178'],
 ['o9_38928', (1, 1), 'K11n172'],
 ['o9_38928', (2, 1), 'L10a105', (-2, 1), 0],
 ['o9_38928', (2, 1), 'L10a105', (-2, 1), 1],
 ['o9_38928', (2, 1), 'L10n54', (-8, 1), 0],
 ['o9_38928', (2, 1), 'L10n54', (-8, 1), 1],
 ['o9_38928', (2, 1), 'L13n7433', (-3, 1), 1],
 ['o9_39162', (-1, 1), 'L13n9864', (-3, 1), 0],
 ['o9_39162', (1, 1), 'L12n1050'],
 ['o9_39162', (1, 2), 'L12n784', (3, 1), 0],
 ['o9_39162', (1, 4), 'L13n4343', (-7, 4), 0],
 ['o9_39162', (2, 1), 'L10n44', (7, 1), 0],
 ['o9_40363', (-3, 4), 'L13n4363', (-7, 4), 0],
 ['o9_40363', (-1, 1), 'L12n785'],
 ['o9_40363', (-1, 2), 'L11a225', (-3, 1), 0],
 ['o9_40363', (-1, 3), 'L12a1861', (4, 1), 1],
 ['o9_40363', (1, 1), 'L11n419', (7, 1), 1],
 ['o9_40363', (1, 1), 'L13n9451', (3, 1), 1],
 ['o9_40363', (1, 1), 'L14n43377', (2, 1), 1],
 ['o9_40487', (-2, 1), 'L12n1041', (-2, 1), 0],
 ['o9_40487', (-1, 1), 'L12n722', (-3, 1), 0],
 ['o9_40487', (0, 1), 'L11n152'],
 ['o9_40487', (1, 1), 'K11n147'],
 ['o9_40487', (1, 2), 'L12n968', (-3, 1), 0],
 ['o9_40487', (2, 1), 'L11n333', (2, 1), 1],
 ['o9_40487', (3, 1), 'L12n1314', (7, 1), 0],
 ['o9_40504', (-2, 1), 'L12n1037', (-2, 1), 0],
 ['o9_40504', (-1, 1), 'L12n715', (-3, 1), 0],
 ['o9_40504', (0, 1), 'L11n179'],
 ['o9_40504', (1, 1), 'K11n166'],
 ['o9_40504', (2, 1), 'L10a146', (-2, 1), 1],
 ['o9_40504', (2, 1), 'L10a146', (-2, 1), 2],
 ['o9_40504', (2, 1), 'L13n7421', (-3, 1), 1],
 ['o9_40504', (2, 1), 'L13n8521', (5, 1), 1],
 ['o9_40582', (-1, 1), 'L10n44', (-5, 3), 0],
 ['o9_40582', (0, 1), 'L13n4413'],
 ['o9_40582', (1, 1), 'K13n2958'],
 ['o9_40582', (1, 2), 'L12n996', (3, 1), 0],
 ['o9_40582', (2, 1), 'L13n9833', (3, 1), 0],
 ['o9_40582', (4, 1), 'L11n350', (-5, 1), 1],
 ['o9_42675', (-2, 1), 'L10n24', (6, 1), 1],
 ['o9_42675', (-2, 1), 'L11n223', (-2, 1), 0],
 ['o9_42675', (-2, 1), 'L13n5311', (2, 1), 0],
 ['o9_42675', (-2, 1), 'L13n9832', (8, 3), 1],
 ['o9_42675', (-1, 1), 'K12n730'],
 ['o9_42675', (0, 1), 'L12n702'],
 ['o9_42675', (1, 1), 'L14n24428', (5, 3), 0],
 ['o9_42675', (2, 1), 'L13n7552', (-2, 1), 1],
 ['t12533', (-3, 1), 'L11n350', (-4, 1), 1],
 ['t12533', (-2, 1), 'L12n722', (3, 1), 0],
 ['t12533', (-1, 1), 'L12n789'],
 ['t12533', (-1, 2), 'L11n192', (-3, 1), 0],
 ['t12533', (0, 1), 'K12n407'],
 ['t12533', (1, 1), 'L13n7360', (2, 1), 1],
 ['t12681', (-2, 3), 'L13n4363', (-5, 3), 0],
 ['t12681', (-1, 1), 'L11n172'],
 ['t12681', (-1, 2), 'L10a81', (3, 1), 0],
 ['t12681', (-1, 3), 'L11a282', (-4, 1), 0],
 ['t12681', (1, 1), 'L11n419', (5, 1), 1],
 ['t12681', (1, 1), 'L12n1907', (3, 1), 1],
 ['t12681', (1, 1), 'L13n7356', (2, 1), 1]]
In [12]:
len(branching_sets)
Out[12]:
63

Thus we have found all branching sets for all possible quotients of all symmetric fillings. Since non of these is an alternating knot in the 3-sphere this finishs the proof that no asymmetric L-space knot in the SnapPy census admits an alternating surgery.