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av_fq_isog • Show schema
{'abvar_count': 4999, 'abvar_counts': [4999, 24990001, 128100854704, 646172078607225, 3255243547403335279, 16409828975895318927616, 82721210695585517090188399, 416997601213797614458654317225, 2102085018129621278380262958102064, 10596610552911050337647068573286007841], 'abvar_counts_str': '4999 24990001 128100854704 646172078607225 3255243547403335279 16409828975895318927616 82721210695585517090188399 416997601213797614458654317225 2102085018129621278380262958102064 10596610552911050337647068573286007841 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.201036467859289, 0.798963532140711], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 72, 'curve_counts': [72, 4956, 357912, 25428148, 1804229352, 128101425486, 9095120158392, 645753497327908, 45848500718449032, 3255243543796789356], 'curve_counts_str': '72 4956 357912 25428148 1804229352 128101425486 9095120158392 645753497327908 45848500718449032 3255243543796789356 ', 'curves': ['y^2=56*x^6+16*x^5+4*x^4+15*x^3+14*x^2+54*x+58', 'y^2=65*x^6+3*x^5+60*x^4+9*x^3+51*x^2+23*x+42', 'y^2=29*x^6+21*x^5+65*x^4+63*x^3+2*x^2+19*x+10', 'y^2=25*x^6+14*x^5+23*x^4+66*x^3+24*x^2+39*x+59', 'y^2=16*x^6+65*x^5+2*x^4+19*x^3+26*x^2+13*x+55', 'y^2=41*x^6+29*x^5+14*x^4+62*x^3+40*x^2+20*x+30', 'y^2=9*x^6+x^5+58*x^4+68*x^3+61*x^2+15*x+26', 'y^2=63*x^6+7*x^5+51*x^4+50*x^3+x^2+34*x+40', 'y^2=16*x^6+48*x^5+49*x^4+26*x^3+56*x^2+9*x+32', 'y^2=41*x^6+52*x^5+59*x^4+40*x^3+37*x^2+63*x+11', 'y^2=15*x^6+9*x^5+70*x^4+38*x^3+65*x^2+30*x+27', 'y^2=34*x^6+63*x^5+64*x^4+53*x^3+29*x^2+68*x+47', 'y^2=41*x^6+4*x^5+41*x^4+68*x^3+3*x^2+54*x+5', 'y^2=62*x^6+29*x^5+70*x^4+49*x^3+24*x^2+49*x+15', 'y^2=8*x^6+61*x^5+64*x^4+59*x^3+26*x^2+59*x+34', 'y^2=12*x^6+46*x^5+8*x^4+21*x^3+7*x^2+33*x+33', 'y^2=11*x^6+38*x^5+58*x^4+43*x^3+45*x^2+9*x+48', 'y^2=6*x^6+53*x^5+51*x^4+17*x^3+31*x^2+63*x+52', 'y^2=58*x^6+17*x^5+5*x^4+51*x^3+57*x^2+22*x+20', 'y^2=51*x^6+48*x^5+35*x^4+2*x^3+44*x^2+12*x+69', 'y^2=10*x^6+x^5+57*x^4+x^3+34*x^2+8*x+7', 'y^2=70*x^6+7*x^5+44*x^4+7*x^3+25*x^2+56*x+49', 'y^2=7*x^6+54*x^5+60*x^4+56*x^3+2*x^2+62*x+67', 'y^2=49*x^6+23*x^5+65*x^4+37*x^3+14*x^2+8*x+43', 'y^2=4*x^6+49*x^5+52*x^4+37*x^3+40*x^2+28*x+58', 'y^2=28*x^6+59*x^5+9*x^4+46*x^3+67*x^2+54*x+51', 'y^2=43*x^6+62*x^5+64*x^4+28*x^3+32*x^2+67*x+49', 'y^2=17*x^6+8*x^5+22*x^4+54*x^3+11*x^2+43*x+59', 'y^2=2*x^6+55*x^5+19*x^4+51*x^3+30*x^2+47*x+37', 'y^2=14*x^6+30*x^5+62*x^4+2*x^3+68*x^2+45*x+46', 'y^2=52*x^6+40*x^5+49*x^4+69*x^3+37*x^2+5*x+15', 'y^2=9*x^6+67*x^5+59*x^4+57*x^3+46*x^2+35*x+34', 'y^2=44*x^6+4*x^5+28*x^4+26*x^3+4*x^2+26*x+43', 'y^2=24*x^6+28*x^5+54*x^4+40*x^3+28*x^2+40*x+17', 'y^2=70*x^6+62*x^5+12*x^4+39*x^3+62*x^2+45*x+66', 'y^2=64*x^6+8*x^5+13*x^4+60*x^3+8*x^2+31*x+36', 'y^2=21*x^6+47*x^5+29*x^4+60*x^3+61*x^2+31*x+32', 'y^2=61*x^6+48*x^5+63*x^4+58*x^3+58*x^2+38*x+50', 'y^2=2*x^6+53*x^5+46*x^4+10*x^3+47*x^2+39*x+44', 'y^2=14*x^6+16*x^5+38*x^4+70*x^3+45*x^2+60*x+24', 'y^2=66*x^6+63*x^5+54*x^4+27*x^3+6*x^2+36*x+38', 'y^2=36*x^6+15*x^5+23*x^4+47*x^3+42*x^2+39*x+53', 'y^2=62*x^6+18*x^5+65*x^4+37*x^3+6*x^2+18*x+9', 'y^2=62*x^6+31*x^5+16*x^4+23*x^3+37*x^2+12*x+16', 'y^2=8*x^6+4*x^5+41*x^4+19*x^3+46*x^2+13*x+41', 'y^2=12*x^6+35*x^5+2*x^4+24*x^3+61*x^2+23*x+62', 'y^2=61*x^6+15*x^5+23*x^4+54*x^3+36*x^2+4*x+2', 'y^2=7*x^6+42*x^5+50*x^4+31*x^3+61*x^2+67*x+38', 'y^2=29*x^6+54*x^5+4*x^4+35*x^3+45*x^2+26*x+59', 'y^2=61*x^6+23*x^5+28*x^4+32*x^3+31*x^2+40*x+58', 'y^2=61*x^6+41*x^5+62*x^4+47*x^2+24*x+70', 'y^2=x^6+3*x^5+8*x^4+45*x^2+26*x+64', 'y^2=25*x^6+10*x^5+20*x^4+53*x^3+7*x^2+69*x+15', 'y^2=33*x^6+70*x^5+69*x^4+16*x^3+49*x^2+57*x+34', 'y^2=54*x^6+10*x^5+63*x^4+52*x^3+41*x^2+64*x+32', 'y^2=23*x^6+70*x^5+15*x^4+9*x^3+3*x^2+22*x+11', 'y^2=17*x^6+27*x^5+29*x^4+36*x^3+x^2+12*x+36', 'y^2=48*x^6+47*x^5+61*x^4+39*x^3+7*x^2+13*x+39', 'y^2=68*x^6+56*x^5+13*x^4+11*x^3+43*x^2+53*x+70', 'y^2=50*x^6+37*x^5+20*x^4+6*x^3+17*x^2+16*x+64', 'y^2=69*x^6+24*x^5+x^4+18*x^3+40*x^2+30*x+49', 'y^2=57*x^6+26*x^5+7*x^4+55*x^3+67*x^2+68*x+59', 'y^2=43*x^6+45*x^5+14*x^4+68*x^3+14*x^2+63*x+63', 'y^2=17*x^6+31*x^5+27*x^4+50*x^3+27*x^2+15*x+15', 'y^2=57*x^6+52*x^5+3*x^4+x^3+24*x^2+27*x+2', 'y^2=44*x^6+9*x^5+21*x^4+7*x^3+26*x^2+47*x+14', 'y^2=15*x^6+50*x^5+30*x^4+28*x^3+59*x^2+11*x+36', 'y^2=34*x^6+66*x^5+68*x^4+54*x^3+58*x^2+6*x+39', 'y^2=2*x^6+59*x^5+33*x^4+42*x^3+9*x^2+20*x+35', 'y^2=14*x^6+58*x^5+18*x^4+10*x^3+63*x^2+69*x+32', 'y^2=30*x^6+43*x^5+46*x^4+32*x^3+60*x^2+29*x+34', 'y^2=11*x^6+23*x^5+56*x^4+61*x^3+33*x^2+70*x+62', 'y^2=6*x^6+19*x^5+37*x^4+x^3+18*x^2+64*x+8', 'y^2=31*x^6+65*x^5+2*x^4+51*x^3+42*x^2+9*x+64', 'y^2=4*x^6+29*x^5+14*x^4+2*x^3+10*x^2+63*x+22', 'y^2=59*x^6+29*x^5+14*x^4+2*x^3+35*x^2+36*x+42', 'y^2=58*x^6+61*x^5+27*x^4+14*x^3+32*x^2+39*x+10', 'y^2=57*x^6+12*x^5+7*x^4+10*x^3+62*x^2+54*x+50', 'y^2=44*x^6+13*x^5+49*x^4+70*x^3+8*x^2+23*x+66', 'y^2=52*x^6+51*x^5+50*x^4+2*x^3+23*x^2+4*x+25', 'y^2=9*x^6+2*x^5+66*x^4+14*x^3+19*x^2+28*x+33', 'y^2=52*x^6+15*x^5+58*x^4+66*x^3+55*x^2+16*x+2', 'y^2=61*x^6+66*x^5+23*x^3+35*x^2+42*x+7', 'y^2=x^6+36*x^5+19*x^3+32*x^2+10*x+49', 'y^2=30*x^6+57*x^4+67*x^3+44*x^2+66', 'y^2=17*x^6+x^5+70*x^4+50*x^3+16*x^2+43*x+19', 'y^2=67*x^6+20*x^5+4*x^4+23*x^3+48*x^2+25*x+41', 'y^2=43*x^6+69*x^5+28*x^4+19*x^3+52*x^2+33*x+3', 'y^2=26*x^6+48*x^5+59*x^4+62*x^3+40*x^2+49*x+41', 'y^2=40*x^6+52*x^5+58*x^4+8*x^3+67*x^2+59*x+3', 'y^2=65*x^6+69*x^5+23*x^4+44*x^3+34*x^2+32*x+39', 'y^2=29*x^6+57*x^5+19*x^4+24*x^3+25*x^2+11*x+60', 'y^2=36*x^6+65*x^5+65*x^4+21*x^3+58*x^2+31*x+23', 'y^2=68*x^6+31*x^5+53*x^4+67*x^3+46*x^2+17*x+46', 'y^2=50*x^6+4*x^5+16*x^4+43*x^3+38*x^2+48*x+38', 'y^2=22*x^6+x^5+50*x^4+6*x^3+46*x^2+29*x+8', 'y^2=12*x^6+7*x^5+66*x^4+42*x^3+38*x^2+61*x+56', 'y^2=55*x^6+52*x^5+14*x^4+15*x^3+68*x^2+39*x+61', 'y^2=30*x^6+9*x^5+27*x^4+34*x^3+50*x^2+60*x+1', 'y^2=18*x^6+13*x^5+33*x^4+x^3+54*x^2+53*x+61', 'y^2=21*x^6+67*x^5+62*x^4+49*x^3+37*x^2+63*x+64', 'y^2=29*x^6+12*x^5+50*x^4+30*x^3+6*x^2+20*x+1', 'y^2=61*x^6+13*x^5+66*x^4+68*x^3+42*x^2+69*x+7', 'y^2=58*x^6+31*x^5+21*x^4+24*x^3+44*x^2+22*x+32', 'y^2=51*x^6+4*x^5+5*x^4+26*x^3+24*x^2+12*x+11', 'y^2=63*x^6+42*x^5+17*x^4+55*x^3+8*x^2+31*x+28', 'y^2=15*x^6+10*x^5+48*x^4+30*x^3+56*x^2+4*x+54', 'y^2=18*x^6+46*x^5+42*x^4+27*x^3+47*x^2+56*x+26', 'y^2=55*x^6+38*x^5+10*x^4+47*x^3+45*x^2+37*x+40', 'y^2=60*x^6+66*x^5+64*x^4+43*x^3+69*x^2+59*x+31', 'y^2=67*x^6+14*x^5+14*x^4+66*x^3+53*x^2+55*x+50', 'y^2=43*x^6+27*x^5+27*x^4+36*x^3+16*x^2+30*x+66', 'y^2=10*x^6+59*x^5+34*x^4+61*x^3+21*x^2+11*x+49', 'y^2=70*x^6+58*x^5+25*x^4+x^3+5*x^2+6*x+59', 'y^2=33*x^6+62*x^5+7*x^4+6*x^3+54*x^2+44*x+3', 'y^2=25*x^6+69*x^5+53*x^4+44*x^3+21*x^2+3*x+5', 'y^2=33*x^6+57*x^5+16*x^4+24*x^3+5*x^2+21*x+35', 'y^2=63*x^6+20*x^5+41*x^4+64*x^3+42*x^2+68*x+55', 'y^2=15*x^6+69*x^5+3*x^4+22*x^3+10*x^2+50*x+30', 'y^2=62*x^6+45*x^5+41*x^4+39*x^3+29*x^2+3*x+2', 'y^2=49*x^6+13*x^5+52*x^4+48*x^3+47*x^2+25*x+11', 'y^2=59*x^6+20*x^5+9*x^4+52*x^3+45*x^2+33*x+6', 'y^2=7*x^6+29*x^5+63*x^4+22*x^3+14*x^2+14*x+57', 'y^2=49*x^6+61*x^5+15*x^4+12*x^3+27*x^2+27*x+44'], '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': 4, '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': 2, 'geometric_galois_groups': ['2T1'], 'geometric_number_fields': ['2.0.2035.1'], 'geometric_splitting_field': '2.0.2035.1', 'geometric_splitting_polynomials': [[509, -1, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 124, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 124, 'label': '2.71.a_abr', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 2, 'newton_elevation': 0, 'number_fields': ['4.0.4141225.3'], 'p': 71, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 5, 1, 12], [1, 5, 2, 12], [1, 11, 1, 2], [1, 23, 1, 24]], 'poly': [1, 0, -43, 0, 5041], 'poly_str': '1 0 -43 0 5041 ', 'primitive_models': [], 'principal_polarization_count': 144, 'q': 71, 'real_poly': [1, 0, -185], 'simple_distinct': ['2.71.a_abr'], 'simple_factors': ['2.71.a_abrA'], 'simple_multiplicities': [1], 'singular_primes': ['2,3*F^2-F+4*V+1', '3,F^2+F+2*V-5'], 'size': 288, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.4141225.3', 'splitting_polynomials': [[2401, 0, -87, 0, 1]], 'twist_count': 2, 'twists': [['2.71.a_br', '2.25411681.yji_jzoedv', 4]], 'weak_equivalence_count': 4, 'zfv_index': 36, 'zfv_index_factorization': [[2, 2], [3, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 192, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 9801, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,3*F^2-F+4*V+1', '3,F^2+F+2*V-5']} - av_fq_endalg_factors • Show schema
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av_fq_endalg_data • Show schema
{'brauer_invariants': ['0', '0', '0', '0'], 'center': '4.0.4141225.3', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.71.a_abr', 'galois_group': '4T2', 'places': [['40', '70', '1', '0'], ['53', '70', '1', '0'], ['57', '70', '1', '0'], ['31', '70', '1', '0']]} -
av_fq_endalg_data • Show schema
{'brauer_invariants': ['0', '0'], 'center': '2.0.2035.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.5041.abr', 'galois_group': '2T1', 'places': [['16', '1'], ['54', '1']]}
Abelian variety isogeny class data - 2.71.a_abr