Formats: - HTML - YAML - JSON - 2026-07-17T05:20:12.075408
  • av_fq_isog • Show schema
    {'abvar_count': 8967, 'abvar_counts': [8967, 87437217, 831295132416, 7839443990730009, 73742316823629509727, 693843618528087090610176, 6528365327177159539936413999, 61425365231759530270607393032425, 577951264248655062649000909212175104, 5437943429730723375868979831665616244177], 'abvar_counts_str': '8967 87437217 831295132416 7839443990730009 73742316823629509727 693843618528087090610176 6528365327177159539936413999 61425365231759530270607393032425 577951264248655062649000909212175104 5437943429730723375868979831665616244177 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.141634171923188, 0.74662062792176], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 94, 'curve_counts': [94, 9292, 910834, 88551988, 8587329094, 832973514622, 80798316070006, 7837433579766436, 760231060898112178, 73742412695774839132], 'curve_counts_str': '94 9292 910834 88551988 8587329094 832973514622 80798316070006 7837433579766436 760231060898112178 73742412695774839132 ', 'curves': ['y^2=64*x^6+66*x^5+82*x^4+44*x^3+21*x^2+76*x+29', 'y^2=93*x^6+x^5+95*x^4+8*x^3+52*x^2+40*x+24', 'y^2=68*x^6+59*x^5+58*x^4+64*x^3+40*x^2+49*x+26', 'y^2=87*x^6+31*x^5+27*x^4+50*x^3+55*x^2+63*x+88', 'y^2=92*x^6+38*x^5+12*x^4+47*x^3+16*x^2+40*x+64', 'y^2=12*x^6+59*x^5+50*x^4+3*x^3+70*x^2+34*x+59', 'y^2=5*x^6+45*x^5+60*x^4+93*x^3+58*x^2+50*x+76', 'y^2=44*x^6+2*x^5+55*x^4+86*x^3+86*x^2+15*x+73', 'y^2=39*x^6+66*x^5+64*x^3+87*x^2+25*x+43', 'y^2=42*x^6+17*x^5+74*x^4+62*x^3+84*x^2+52*x+68', 'y^2=91*x^6+94*x^5+89*x^4+92*x^3+54*x^2+10*x+57', 'y^2=44*x^6+78*x^5+82*x^4+3*x^3+61*x^2+72*x+30', 'y^2=69*x^6+49*x^5+22*x^4+35*x^3+70*x^2+53*x+32', 'y^2=29*x^6+85*x^5+13*x^4+55*x^3+89*x^2+35*x+45', 'y^2=31*x^6+12*x^5+39*x^4+49*x^3+74*x^2+64*x+14', 'y^2=64*x^6+64*x^5+45*x^4+55*x^3+11*x^2+57*x+10', 'y^2=6*x^6+76*x^5+14*x^4+94*x^3+35*x^2+92*x+31', 'y^2=8*x^6+67*x^5+20*x^4+41*x^3+8*x^2+66*x+88', 'y^2=36*x^6+60*x^5+77*x^4+25*x^3+52*x^2+89*x+12', 'y^2=91*x^6+69*x^5+25*x^4+82*x^3+78*x^2+x+46', 'y^2=x^6+89*x^5+10*x^4+86*x^3+67*x^2+72*x+64', 'y^2=60*x^6+50*x^5+23*x^4+68*x^3+50*x^2+39*x+25', 'y^2=58*x^6+46*x^5+44*x^4+19*x^3+89*x^2+67*x+89', 'y^2=71*x^6+84*x^5+27*x^4+50*x^3+34*x^2+43*x+57', 'y^2=78*x^6+49*x^5+95*x^4+69*x^3+34*x^2+83*x+78', 'y^2=73*x^6+86*x^5+96*x^4+8*x^3+7*x^2+68*x+96', 'y^2=16*x^6+82*x^5+17*x^4+92*x^3+25*x^2+15*x+90', 'y^2=16*x^6+34*x^5+7*x^4+95*x^3+24*x^2+62*x+63', 'y^2=26*x^6+49*x^5+96*x^4+20*x^3+12*x^2+47*x+22', 'y^2=55*x^6+78*x^5+21*x^4+x^3+85*x^2+78', 'y^2=82*x^6+28*x^5+29*x^4+21*x^3+18*x^2+80*x+32', 'y^2=38*x^6+33*x^5+36*x^4+69*x^3+45*x^2+20*x+42', 'y^2=45*x^6+26*x^5+96*x^4+96*x^3+21*x^2+95*x+81', 'y^2=x^6+92*x^5+80*x^4+71*x^3+2*x^2+77*x+37', 'y^2=24*x^6+51*x^5+56*x^4+35*x^3+32*x^2+20*x+45', 'y^2=30*x^6+28*x^5+91*x^4+91*x^3+40*x^2+63*x+70', 'y^2=77*x^6+81*x^5+25*x^4+25*x^3+93*x^2+7*x+1', 'y^2=53*x^6+49*x^5+24*x^4+74*x^3+21*x^2+56*x+28', 'y^2=23*x^6+33*x^5+57*x^4+54*x^3+77*x^2+48*x+38', 'y^2=95*x^6+22*x^5+92*x^4+10*x^3+10*x^2+10*x+27', 'y^2=82*x^6+78*x^4+9*x^3+8*x^2+81*x+47', 'y^2=21*x^6+43*x^5+36*x^4+x^3+90*x^2+4*x+7', 'y^2=55*x^6+16*x^5+68*x^4+49*x^3+88*x^2+32*x+66', 'y^2=84*x^6+12*x^5+49*x^4+28*x^3+16*x^2+45*x+41', 'y^2=51*x^6+57*x^5+26*x^4+61*x^3+43*x^2+81*x+67', 'y^2=47*x^6+77*x^5+14*x^4+36*x^3+49*x^2+31*x+59', 'y^2=50*x^6+45*x^5+73*x^4+15*x^3+24*x^2+57*x+78', 'y^2=46*x^6+91*x^5+14*x^4+31*x^3+7*x^2+11*x+56', 'y^2=80*x^6+13*x^5+73*x^4+24*x^3+33*x^2+88*x+34', 'y^2=34*x^6+38*x^5+24*x^4+85*x^3+20*x^2+78*x+50', 'y^2=29*x^6+77*x^5+74*x^4+80*x^3+60*x^2+78*x+25', 'y^2=89*x^6+81*x^5+40*x^4+83*x^3+86*x^2+31*x+36', 'y^2=47*x^6+12*x^5+66*x^4+59*x^3+14*x^2+62*x+46', 'y^2=6*x^6+49*x^5+62*x^4+3*x^3+64*x^2+88*x+59', 'y^2=68*x^6+72*x^5+26*x^4+20*x^3+86*x^2+73*x+4', 'y^2=75*x^6+23*x^5+50*x^4+69*x^3+71*x^2+72*x+23', 'y^2=86*x^6+73*x^5+28*x^4+79*x^3+76*x^2+23*x+54', 'y^2=82*x^6+69*x^5+69*x^4+43*x^3+9*x^2+60*x+26', 'y^2=53*x^6+69*x^5+2*x^4+95*x^3+79*x^2+90*x+68', 'y^2=64*x^6+19*x^5+68*x^4+23*x^3+91*x^2+11*x+53', 'y^2=5*x^6+43*x^5+16*x^4+25*x^3+47*x^2+20*x+6', 'y^2=43*x^6+34*x^5+90*x^4+28*x^3+95*x^2+11*x+28', 'y^2=28*x^6+25*x^5+33*x^4+9*x^3+50*x^2+4*x+58', 'y^2=13*x^6+34*x^5+14*x^4+37*x^3+6*x^2+9*x+88', 'y^2=77*x^6+22*x^5+30*x^4+93*x^3+17*x^2+33*x+35', 'y^2=19*x^6+93*x^5+12*x^4+46*x^3+65*x^2+56*x+67', 'y^2=17*x^6+96*x^5+16*x^4+91*x^3+7*x^2+10*x+65', 'y^2=9*x^6+86*x^5+55*x^4+82*x^3+22*x^2+79*x+62', 'y^2=63*x^6+67*x^5+20*x^4+5*x^3+28*x^2+48*x+23', 'y^2=31*x^6+57*x^5+91*x^4+61*x^3+84*x^2+56*x+21', 'y^2=53*x^6+79*x^5+x^4+76*x^3+84*x^2+12*x+94', 'y^2=12*x^6+70*x^5+90*x^4+56*x^3+51*x^2+2*x+30', 'y^2=40*x^6+16*x^5+75*x^4+89*x^3+88*x^2+12*x+91', 'y^2=54*x^6+94*x^5+83*x^4+12*x^3+5*x^2+47*x+66', 'y^2=78*x^6+19*x^5+48*x^4+26*x^3+18*x^2+94*x+40', 'y^2=54*x^6+86*x^5+71*x^4+92*x^3+61*x^2+76*x+81', 'y^2=86*x^6+10*x^5+10*x^4+78*x^3+63*x^2+27*x+49', 'y^2=92*x^6+93*x^5+43*x^4+60*x^3+10*x^2+76*x+25', 'y^2=82*x^6+39*x^5+27*x^4+81*x^3+92*x^2+43*x+25', 'y^2=55*x^6+22*x^5+84*x^4+49*x^3+52*x^2+73*x+93', 'y^2=77*x^6+12*x^5+89*x^4+79*x^3+21*x^2+78*x+28', 'y^2=9*x^6+16*x^5+48*x^4+91*x^3+18*x^2+73*x+72', 'y^2=85*x^6+93*x^5+20*x^4+13*x^3+42*x^2+52*x+95', 'y^2=44*x^6+83*x^5+34*x^4+24*x^3+68*x^2+27*x+48', 'y^2=14*x^6+37*x^5+81*x^4+24*x^3+19*x^2+8*x+75', 'y^2=60*x^6+87*x^5+16*x^4+96*x^3+23*x^2+41*x+43', 'y^2=13*x^6+33*x^5+36*x^4+87*x^3+53*x^2+72*x+12', 'y^2=67*x^6+53*x^5+23*x^4+50*x^3+43*x^2+74*x+22', 'y^2=73*x^6+68*x^5+88*x^4+57*x^3+61*x^2+76*x+21', 'y^2=36*x^6+73*x^5+45*x^4+40*x^3+26*x^2+41*x+76', 'y^2=61*x^6+92*x^5+67*x^4+76*x^3+79*x^2+84*x+56', 'y^2=13*x^6+50*x^5+27*x^4+65*x^3+21*x^2+3*x+4', 'y^2=96*x^6+51*x^5+43*x^4+34*x^3+54*x^2+53*x+58', 'y^2=19*x^6+73*x^5+45*x^4+56*x^3+53*x^2+61*x+33', 'y^2=13*x^6+21*x^5+18*x^4+83*x^3+45*x^2+23*x+85', 'y^2=28*x^6+90*x^5+33*x^4+49*x^3+78*x^2+16*x+59', 'y^2=40*x^6+78*x^5+46*x^4+18*x^3+66*x^2+49*x+65', 'y^2=21*x^6+50*x^5+75*x^4+8*x^3+15*x^2+65*x+2', 'y^2=67*x^6+37*x^5+17*x^4+37*x^3+82*x^2+93*x+90', 'y^2=58*x^6+52*x^5+64*x^4+86*x^3+77*x^2+34*x+57', 'y^2=85*x^6+51*x^5+19*x^4+51*x^3+71*x^2+2*x+10', 'y^2=66*x^6+47*x^5+73*x^4+2*x^3+60*x^2+42*x+78', 'y^2=76*x^6+38*x^5+18*x^4+92*x^3+37*x^2+4*x+76', 'y^2=5*x^6+38*x^5+92*x^4+84*x^3+18*x^2+93*x+6', 'y^2=30*x^6+71*x^5+71*x^4+46*x^3+55*x^2+28*x+33', 'y^2=32*x^6+30*x^5+62*x^4+22*x^3+16*x^2+57*x+33', 'y^2=83*x^6+46*x^5+30*x^4+32*x^3+24*x^2+74*x+78', 'y^2=36*x^6+81*x^5+89*x^4+21*x^3+10*x^2+52*x+45', 'y^2=19*x^6+94*x^5+36*x^4+12*x^3+30*x^2+90*x+34', 'y^2=52*x^6+8*x^5+66*x^4+89*x^3+47*x^2+73*x+91', 'y^2=80*x^6+66*x^5+37*x^4+94*x^3+60*x^2+13*x+84', 'y^2=12*x^6+75*x^5+34*x^4+91*x^3+67*x^2+46*x+46'], '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': 2, 'g': 2, 'galois_groups': ['4T3'], 'geom_dim1_distinct': 0, 'geom_dim1_factors': 0, 'geom_dim2_distinct': 1, 'geom_dim2_factors': 1, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['4T3'], 'geometric_number_fields': ['4.0.882956241.1'], 'geometric_splitting_field': '4.0.882956241.1', 'geometric_splitting_polynomials': [[907, -68, 69, -2, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 112, 'is_cyclic': True, 'is_geometrically_simple': True, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': True, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 112, 'label': '2.97.ae_abz', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['4.0.882956241.1'], 'p': 97, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 3, 1, 2], [1, 7, 1, 42], [1, 47, 1, 42]], 'poly': [1, -4, -51, -388, 9409], 'poly_str': '1 -4 -51 -388 9409 ', 'primitive_models': [], 'principal_polarization_count': 112, 'q': 97, 'real_poly': [1, -4, -245], 'simple_distinct': ['2.97.ae_abz'], 'simple_factors': ['2.97.ae_abzA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-F-V-5'], 'size': 112, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.882956241.1', 'splitting_polynomials': [[907, -68, 69, -2, 1]], 'twist_count': 2, 'twists': [['2.97.e_abz', '2.9409.aeo_bbcl', 2]], 'weak_equivalence_count': 2, 'zfv_index': 4, 'zfv_index_factorization': [[2, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_pic_size': 84, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 14241, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-F-V-5']}
  • av_fq_endalg_factors • Show schema
    {'base_label': '2.97.ae_abz', 'extension_degree': 1, 'extension_label': '2.97.ae_abz', 'multiplicity': 1}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '4.0.882956241.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.97.ae_abz', 'galois_group': '4T3', 'places': [['37', '94', '1', '0'], ['35', '1', '1', '0']]}