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{'abvar_count': 6192, 'abvar_counts': [6192, 28260288, 152174889216, 806175244594944, 4297560176529101232, 22901931807121208217600, 122045086249850329681609008, 650377915192865680803570760704, 3465863720918660212791307612326144, 18469587758626819042563545685189908928], 'abvar_counts_str': '6192 28260288 152174889216 806175244594944 4297560176529101232 22901931807121208217600 122045086249850329681609008 650377915192865680803570760704 3465863720918660212791307612326144 18469587758626819042563545685189908928 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.389279142100031, 0.944054191233302], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 85, 'curve_counts': [85, 5305, 391174, 28388209, 2073039925, 151333458190, 11047405055485, 806460135758689, 58871586697559062, 4297625826560340025], 'curve_counts_str': '85 5305 391174 28388209 2073039925 151333458190 11047405055485 806460135758689 58871586697559062 4297625826560340025 ', 'curves': ['y^2=29*x^6+50*x^5+55*x^4+38*x^3+42*x^2+21*x+43', 'y^2=54*x^6+63*x^5+65*x^4+43*x^3+63*x^2+26*x+38', 'y^2=71*x^6+41*x^5+60*x^4+23*x^3+10*x^2+32*x+58', 'y^2=17*x^6+x^5+31*x^4+4*x^3+40*x^2+21*x+3', 'y^2=15*x^6+12*x^5+8*x^4+55*x^3+70*x^2+12*x+10', 'y^2=58*x^6+21*x^5+45*x^4+64*x^3+x^2+14*x+62', 'y^2=43*x^6+58*x^5+16*x^4+34*x^3+44*x^2+71*x+24', 'y^2=35*x^6+44*x^5+25*x^4+9*x^3+32*x^2+37*x+8', 'y^2=28*x^6+x^5+31*x^4+x^3+51*x^2+33*x+49', 'y^2=50*x^5+43*x^4+57*x^3+49*x^2+57*x+18', 'y^2=72*x^6+21*x^5+69*x^4+40*x^3+49*x^2+17*x+21', 'y^2=31*x^6+21*x^5+29*x^4+20*x^3+44*x^2+24*x+26', 'y^2=9*x^6+15*x^5+62*x^4+71*x^3+34*x^2+48*x+56', 'y^2=71*x^6+37*x^5+37*x^4+36*x^3+54*x^2+35*x+9', 'y^2=51*x^6+54*x^5+40*x^4+66*x^3+19*x^2+2*x+47', 'y^2=5*x^6+3*x^5+16*x^4+65*x^3+34*x^2+70*x+71', 'y^2=8*x^6+25*x^5+32*x^4+17*x^3+66*x^2+39*x+61', 'y^2=44*x^6+14*x^5+26*x^4+34*x^3+61*x^2+65*x+60', 'y^2=25*x^6+21*x^5+3*x^4+6*x^3+15*x^2+44*x+71', 'y^2=36*x^6+32*x^5+3*x^4+20*x^3+8*x^2+6*x+34', 'y^2=62*x^5+37*x^4+23*x^3+22*x^2+27*x+25', 'y^2=4*x^6+12*x^5+44*x^4+55*x^2+12*x+23', 'y^2=45*x^6+44*x^5+26*x^4+64*x^3+64*x^2+63*x+10', 'y^2=64*x^6+15*x^5+24*x^4+69*x^3+7*x^2+11*x+56', 'y^2=62*x^6+9*x^5+68*x^4+34*x^3+70*x^2+36*x+27', 'y^2=52*x^6+65*x^5+72*x^4+65*x^3+62*x^2+3*x+18', 'y^2=39*x^6+25*x^5+40*x^4+29*x^3+14*x^2+43*x+8', 'y^2=37*x^6+18*x^5+28*x^4+35*x^3+61*x^2+19*x+15', 'y^2=25*x^6+45*x^5+33*x^4+46*x^3+56*x^2+5*x+59', 'y^2=36*x^6+30*x^5+35*x^4+55*x^3+7*x^2+15*x+58', 'y^2=x^6+5*x^3+55', 'y^2=38*x^6+5*x^5+22*x^4+9*x^3+30*x^2+18*x+15', 'y^2=67*x^5+46*x^4+44*x^3+47*x^2+47*x+21', 'y^2=19*x^6+32*x^5+72*x^4+61*x^3+22*x^2+24*x+7', 'y^2=48*x^6+59*x^5+31*x^4+32*x^3+16*x^2+15*x+51', 'y^2=32*x^6+51*x^5+17*x^4+37*x^3+31*x^2+45*x+15', 'y^2=54*x^6+57*x^5+23*x^4+28*x^3+33*x^2+70*x+36', 'y^2=56*x^6+39*x^5+31*x^4+40*x^3+22*x^2+62*x+38', 'y^2=46*x^6+22*x^5+65*x^4+59*x^3+70*x^2+41*x+56', 'y^2=69*x^6+41*x^5+53*x^4+44*x^3+44*x^2+15*x+44', 'y^2=19*x^6+42*x^5+24*x^4+72*x^3+40*x^2+56*x+1', 'y^2=59*x^6+63*x^5+54*x^4+44*x^3+70*x^2+48*x+2', 'y^2=70*x^6+11*x^5+34*x^4+53*x^3+35*x^2+4*x+9', 'y^2=8*x^6+4*x^5+56*x^4+49*x^3+30*x^2+52*x+41', 'y^2=25*x^6+41*x^5+2*x^4+42*x^3+44*x^2+42*x+56', 'y^2=24*x^6+23*x^5+69*x^4+53*x^3+40*x^2+33*x+46', 'y^2=25*x^6+x^5+39*x^4+23*x^3+54*x^2+6*x+10', 'y^2=36*x^6+42*x^5+35*x^4+49*x^3+64*x^2+27*x+59', 'y^2=36*x^6+29*x^5+56*x^4+40*x^3+23*x^2+11*x+20', 'y^2=62*x^6+30*x^5+15*x^4+13*x^3+31*x^2+16*x+61', 'y^2=17*x^6+25*x^5+38*x^4+52*x^3+8*x^2+23*x+29', 'y^2=72*x^6+62*x^5+32*x^4+45*x^3+54*x^2+34*x+23', 'y^2=27*x^6+70*x^5+21*x^4+21*x^3+51*x^2+48*x+12', 'y^2=18*x^6+33*x^5+41*x^4+16*x^3+15*x^2+63*x+17', 'y^2=42*x^6+47*x^5+50*x^3+19*x^2+65*x+61', 'y^2=12*x^6+27*x^5+32*x^4+50*x^3+53*x^2+24*x+45', 'y^2=16*x^6+42*x^5+8*x^4+24*x^3+39*x^2+32*x+27', 'y^2=31*x^6+31*x^5+6*x^4+52*x^3+32*x^2+12*x+8', 'y^2=68*x^6+63*x^5+10*x^4+66*x^3+37*x^2+31*x+7', 'y^2=63*x^6+47*x^5+5*x^4+61*x^3+33*x^2+23*x+30', 'y^2=26*x^6+68*x^5+41*x^4+37*x^3+43*x^2+58*x+38', 'y^2=44*x^6+48*x^5+31*x^4+28*x^3+38*x^2+36*x+28', 'y^2=45*x^6+3*x^5+6*x^4+24*x^3+x^2+42*x+9', 'y^2=45*x^6+25*x^5+72*x^4+5*x^3+x^2+25*x+46', 'y^2=8*x^6+12*x^5+21*x^4+59*x^3+58*x^2+29*x+12', 'y^2=56*x^6+45*x^5+25*x^4+41*x^3+19*x^2+23*x+3', 'y^2=47*x^6+63*x^5+13*x^4+53*x^3+57*x^2+66*x+44', 'y^2=45*x^6+41*x^5+72*x^4+2*x^3+69*x^2+70*x+8', 'y^2=18*x^6+21*x^5+23*x^4+13*x^3+44*x^2+6*x+53', 'y^2=59*x^6+6*x^5+41*x^4+49*x^3+44*x^2+49*x+56', 'y^2=72*x^6+48*x^5+42*x^4+69*x^3+30*x^2+34*x+50', 'y^2=34*x^6+55*x^5+41*x^4+28*x^3+38*x^2+3*x+39', 'y^2=49*x^6+15*x^5+52*x^4+61*x^3+56*x^2+67*x+65', 'y^2=42*x^6+37*x^5+61*x^4+19*x^3+23*x^2+16*x+19', 'y^2=52*x^6+23*x^5+28*x^4+61*x^3+59*x^2+45*x+43', 'y^2=5*x^6+50*x^5+61*x^4+47*x^3+61*x^2+69*x+35', 'y^2=19*x^6+50*x^5+6*x^4+72*x^3+25*x^2+61*x+26', 'y^2=16*x^6+16*x^5+31*x^4+50*x^3+43*x^2+17*x+63', 'y^2=58*x^6+40*x^5+71*x^4+22*x^3+3*x^2+19*x+27', 'y^2=6*x^6+55*x^5+52*x^4+70*x^3+23*x^2+8*x+62', 'y^2=72*x^6+48*x^5+22*x^4+18*x^3+47*x^2+60*x+60', 'y^2=24*x^6+60*x^5+48*x^4+14*x^3+36*x^2+30*x+41', 'y^2=32*x^6+x^5+12*x^4+34*x^3+43*x^2+39*x+49', 'y^2=4*x^6+59*x^5+28*x^4+58*x^3+45*x^2+29*x+71', 'y^2=15*x^6+10*x^5+56*x^4+15*x^3+69*x^2+15*x+32', 'y^2=42*x^6+48*x^5+2*x^4+67*x^3+20*x^2+5*x+6', 'y^2=15*x^6+59*x^5+11*x^4+20*x^3+65*x^2+4*x+72', 'y^2=49*x^6+38*x^5+32*x^4+15*x^3+48*x^2+61*x+35', 'y^2=8*x^6+62*x^5+x^4+32*x^3+71*x^2+46*x+19', 'y^2=59*x^6+22*x^5+5*x^4+36*x^3+31*x^2+12*x+34', 'y^2=16*x^6+16*x^5+6*x^4+32*x^3+14*x^2+19*x+65', 'y^2=71*x^6+37*x^5+45*x^4+57*x^3+7*x^2+17*x+69', 'y^2=38*x^6+62*x^5+25*x^4+41*x^3+26*x^2+5*x+24', 'y^2=48*x^6+17*x^5+5*x^4+57*x^3+53*x^2+59*x+12', 'y^2=34*x^6+59*x^5+45*x^4+3*x^3+52*x^2+18*x+3', 'y^2=53*x^6+6*x^5+20*x^4+37*x^3+59*x^2+58*x+25', 'y^2=16*x^6+23*x^5+54*x^4+21*x^3+18*x^2+44*x+33', 'y^2=34*x^6+44*x^5+36*x^4+61*x^3+20*x^2+27*x+31', 'y^2=23*x^6+63*x^5+33*x^4+18*x^3+3*x^2+34*x+65', 'y^2=56*x^6+33*x^5+35*x^4+7*x^3+8*x^2+57*x+49', 'y^2=49*x^6+65*x^5+9*x^4+31*x^3+50*x^2+22*x+67', 'y^2=38*x^6+42*x^5+42*x^4+30*x^3+23*x^2+17*x+58', 'y^2=4*x^5+24*x^4+3*x^3+65*x^2+12*x+70', 'y^2=52*x^6+30*x^5+27*x^4+20*x^3+50*x^2+47*x+55', 'y^2=65*x^6+11*x^5+14*x^4+44*x^3+34*x^2+69*x+31', 'y^2=50*x^6+25*x^5+43*x^4+7*x^3+10*x^2+11*x+6', 'y^2=53*x^6+28*x^5+53*x^4+60*x^3+66*x^2+13*x+58', 'y^2=36*x^6+60*x^5+x^4+68*x^3+14*x^2+34*x+59', 'y^2=11*x^6+55*x^5+5*x^4+72*x^3+48*x^2+71*x+69', 'y^2=72*x^6+13*x^5+8*x^4+44*x^3+13*x^2+15*x+9', 'y^2=38*x^6+23*x^5+28*x^4+63*x^3+36*x^2+66*x+36', 'y^2=x^6+5*x^3+67', 'y^2=19*x^6+54*x^5+31*x^4+72*x^3+47*x^2+6*x+61', 'y^2=9*x^6+2*x^5+11*x^4+37*x^3+22*x^2+35*x+8', 'y^2=29*x^6+27*x^5+58*x^4+28*x^3+26*x^2+57*x+11', 'y^2=13*x^6+66*x^5+15*x^4+63*x^2+27*x+2', 'y^2=66*x^6+68*x^5+63*x^4+17*x^3+18*x^2+32*x+19', 'y^2=31*x^6+63*x^5+45*x^4+25*x^3+39*x^2+56*x+45', 'y^2=5*x^6+14*x^5+7*x^4+2*x^3+38*x^2+9*x+12', 'y^2=58*x^6+33*x^5+64*x^4+15*x^3+23*x^2+30*x+53', 'y^2=18*x^6+18*x^4+25*x^3+55*x^2+18*x+18', 'y^2=27*x^6+41*x^5+6*x^4+61*x^3+64*x^2+72*x+58', 'y^2=2*x^6+55*x^5+8*x^4+20*x^3+57*x^2+57*x+66', 'y^2=60*x^6+64*x^5+31*x^4+39*x^3+17*x^2+19*x+35', 'y^2=51*x^6+40*x^5+47*x^4+39*x^3+51*x^2+37*x+53', 'y^2=39*x^6+60*x^5+58*x^4+15*x^3+38*x^2+38*x+48', 'y^2=55*x^6+44*x^5+20*x^4+68*x^3+18*x^2+59*x+4', 'y^2=42*x^6+27*x^5+57*x^4+12*x^3+62*x^2+43*x+29', 'y^2=x^6+x^3+67', 'y^2=62*x^6+61*x^5+63*x^4+31*x^3+15*x^2+9*x+32', 'y^2=69*x^6+55*x^5+71*x^4+71*x^3+41*x^2+59*x+14', 'y^2=3*x^6+45*x^5+33*x^4+47*x^3+15*x^2+36*x+19', 'y^2=61*x^6+57*x^5+54*x^4+63*x^3+14*x^2+65*x+49', 'y^2=48*x^6+15*x^5+61*x^4+42*x^3+21*x^2+25*x+9', 'y^2=33*x^6+20*x^5+58*x^4+37*x^3+8*x^2+10*x+18', 'y^2=66*x^6+45*x^5+48*x^4+12*x^3+47*x^2+43*x+72', 'y^2=57*x^6+26*x^5+54*x^4+21*x^3+56*x^2+36*x+72', 'y^2=24*x^6+20*x^5+37*x^4+63*x^3+18*x^2+56*x+49', 'y^2=64*x^6+13*x^5+23*x^4+55*x^3+69*x^2+26*x+23', 'y^2=61*x^6+44*x^5+13*x^4+32*x^3+6*x^2+46*x+71', 'y^2=5*x^6+40*x^5+19*x^4+57*x^3+43*x^2+26*x+35', 'y^2=37*x^6+60*x^5+43*x^4+72*x^3+33*x^2+5*x+70', 'y^2=66*x^6+8*x^5+68*x^4+35*x^3+18*x^2+59*x+20', 'y^2=2*x^6+27*x^5+48*x^4+39*x^3+41*x^2+63*x+60', 'y^2=3*x^6+15*x^5+47*x^4+8*x^3+13*x^2+x+7', 'y^2=70*x^6+20*x^5+5*x^4+49*x^3+7*x^2+57*x+65', 'y^2=35*x^6+16*x^5+59*x^4+52*x^3+71*x^2+59*x+59', 'y^2=37*x^6+65*x^4+3*x^3+25*x^2+55*x+69', 'y^2=39*x^6+66*x^5+50*x^4+12*x^3+49*x^2+47*x+14', 'y^2=12*x^6+42*x^5+45*x^4+16*x^3+70*x^2+47*x+33', 'y^2=56*x^6+32*x^5+31*x^4+40*x^3+49*x^2+13*x+51', 'y^2=25*x^6+35*x^5+14*x^4+56*x^3+9*x^2+26*x+12', 'y^2=71*x^5+61*x^4+71*x^3+13*x^2+66*x+19', 'y^2=14*x^6+24*x^5+41*x^4+19*x^3+39*x^2+37*x+18', 'y^2=36*x^6+37*x^5+37*x^4+52*x^3+57*x^2+42*x+18', 'y^2=56*x^6+23*x^5+19*x^4+47*x^3+16*x+30', 'y^2=61*x^6+32*x^5+11*x^4+15*x^3+50*x^2+44*x+43', 'y^2=5*x^6+8*x^5+64*x^4+6*x^3+8*x^2+71*x+46', 'y^2=53*x^6+13*x^5+72*x^4+47*x^3+45*x^2+62*x+61', 'y^2=32*x^6+10*x^5+19*x^4+47*x^3+64*x^2+37*x+12', 'y^2=x^6+x^3+19', 'y^2=34*x^6+35*x^5+68*x^4+56*x^3+2*x^2+70*x+50', 'y^2=23*x^6+65*x^5+33*x^4+10*x^3+56*x^2+60*x+56', 'y^2=56*x^6+64*x^5+14*x^4+66*x^3+64*x^2+20*x+49', 'y^2=24*x^6+22*x^5+67*x^4+70*x^3+71*x^2+61*x+2', 'y^2=23*x^6+43*x^5+14*x^4+71*x^3+61*x^2+48*x+52', 'y^2=43*x^6+16*x^5+42*x^4+37*x^3+32*x^2+15*x+24', 'y^2=26*x^6+34*x^5+54*x^4+44*x^3+44*x^2+36*x', 'y^2=68*x^6+42*x^5+49*x^4+28*x^3+28*x^2+56*x+13', 'y^2=10*x^6+21*x^5+63*x^4+8*x^3+51*x^2+7*x+63', 'y^2=30*x^6+8*x^5+21*x^4+4*x^3+12*x^2+17*x+64', 'y^2=29*x^6+17*x^5+56*x^4+44*x^3+27*x^2+44*x+6', 'y^2=8*x^6+66*x^5+35*x^4+21*x^3+31*x^2+17*x+40'], 'dim1_distinct': 0, 'dim1_factors': 0, 'dim2_distinct': 1, 'dim2_factors': 1, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 20, 'g': 2, 'galois_groups': ['4T2'], 'geom_dim1_distinct': 1, 'geom_dim1_factors': 2, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 0, 'geom_dim3_factors': 0, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 2, 'geometric_extension_degree': 3, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.19.1'], 'geometric_splitting_field': '2.0.19.1', 'geometric_splitting_polynomials': [[5, -1, 1]], 'group_structure_count': 6, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 173, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 173, 'label': '2.73.l_bw', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 12, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2, 3], 'number_fields': ['4.0.3249.1'], 'p': 73, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 7, 1, 4], [1, 7, 2, 12]], 'poly': [1, 11, 48, 803, 5329], 'poly_str': '1 11 48 803 5329 ', 'primitive_models': [], 'principal_polarization_count': 173, 'q': 73, 'real_poly': [1, 11, -98], 'simple_distinct': ['2.73.l_bw'], 'simple_factors': ['2.73.l_bwA'], 'simple_multiplicities': [1], 'singular_primes': ['2,3*V+37', '3,-F^2+F-3'], 'size': 165, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.3249.1', 'splitting_polynomials': [[25, -5, -4, -1, 1]], 'twist_count': 6, 'twists': [['2.73.al_bw', '2.5329.az_agyy', 2], ['2.73.aw_kh', '2.389017.dey_egjzy', 3], ['2.73.a_z', '2.151334226289.abrsgi_cebgcuxgo', 6], ['2.73.w_kh', '2.151334226289.abrsgi_cebgcuxgo', 6], ['2.73.a_az', '2.22902048046490258711521.bmqqojesq_bprhoumybagastiao', 12]], 'weak_equivalence_count': 20, 'zfv_index': 432, 'zfv_index_factorization': [[2, 4], [3, 3]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 48, 'zfv_plus_index': 3, 'zfv_plus_index_factorization': [[3, 1]], 'zfv_plus_norm': 2304, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,3*V+37', '3,-F^2+F-3']}
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av_fq_endalg_factors • Show schema
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id: 77745
{'base_label': '2.73.l_bw', 'extension_degree': 1, 'extension_label': '2.73.l_bw', 'multiplicity': 1}
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id: 77746
{'base_label': '2.73.l_bw', 'extension_degree': 3, 'extension_label': '1.389017.bpm', 'multiplicity': 2}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0', '0', '0'], 'center': '4.0.3249.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.73.l_bw', 'galois_group': '4T2', 'places': [['12', '1', '0', '0'], ['38', '1', '0', '0'], ['52', '1', '0', '0'], ['43', '1', '0', '0']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.19.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.389017.bpm', 'galois_group': '2T1', 'places': [['22', '1'], ['50', '1']]}
