Formats: - HTML - YAML - JSON - 2026-07-17T03:39:55.903052
  • av_fq_isog • Show schema
    {'abvar_count': 4011, 'abvar_counts': [4011, 20452089, 90290241216, 406166400355401, 1823036108219717811, 8182742439445644865536, 36732211064864156166201051, 164890967371377180245908274889, 740195508444601615732006107182784, 3322737651886746804013533668595798249], 'abvar_counts_str': '4011 20452089 90290241216 406166400355401 1823036108219717811 8182742439445644865536 36732211064864156166201051 164890967371377180245908274889 740195508444601615732006107182784 3322737651886746804013533668595798249 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.200813477949091, 0.603291390977709], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 60, 'curve_counts': [60, 4556, 300204, 20156020, 1350271980, 90458642342, 6060709279188, 406067698772644, 27206534197365588, 1822837799166565436], 'curve_counts_str': '60 4556 300204 20156020 1350271980 90458642342 6060709279188 406067698772644 27206534197365588 1822837799166565436 ', 'curves': ['y^2=66*x^6+66*x^5+62*x^4+44*x^3+53*x^2+55*x+57', 'y^2=58*x^6+44*x^5+41*x^4+61*x^3+57*x^2+x+36', 'y^2=42*x^6+42*x^5+40*x^4+41*x^3+x^2+5*x+65', 'y^2=52*x^6+51*x^4+x^3+58*x^2+59*x+49', 'y^2=54*x^6+x^5+29*x^4+46*x^3+38*x^2+64*x+32', 'y^2=29*x^6+66*x^5+60*x^3+46*x^2+17*x+43', 'y^2=43*x^6+50*x^5+49*x^4+60*x^3+11*x^2+41*x+5', 'y^2=63*x^6+61*x^5+50*x^4+23*x^3+8*x^2+48*x+47', 'y^2=27*x^6+23*x^5+6*x^4+48*x^3+6*x^2+59*x+9', 'y^2=23*x^6+38*x^5+44*x^4+9*x^3+6*x^2+64*x+61', 'y^2=52*x^6+62*x^5+11*x^4+48*x^3+19*x^2+5*x+38', 'y^2=14*x^6+37*x^5+31*x^4+25*x^3+5*x^2+17*x+32', 'y^2=59*x^6+18*x^5+17*x^4+4*x^2+43*x+12', 'y^2=50*x^6+51*x^5+5*x^4+53*x^3+45*x^2+4*x+39', 'y^2=57*x^6+36*x^5+30*x^4+24*x^3+30*x^2+2*x+39', 'y^2=50*x^6+22*x^5+50*x^4+37*x^3+38*x^2+49*x+53', 'y^2=63*x^6+44*x^5+53*x^4+5*x^3+34*x^2+55*x+58', 'y^2=61*x^6+63*x^5+36*x^4+38*x^3+27*x^2+41*x+35', 'y^2=10*x^6+25*x^5+21*x^4+60*x^3+40*x^2+59*x+40', 'y^2=18*x^6+59*x^5+7*x^4+23*x^3+62*x^2+57*x+23', 'y^2=52*x^6+18*x^5+45*x^4+22*x^3+11*x^2+45*x+50', 'y^2=61*x^6+9*x^5+14*x^3+59*x^2+12*x+62', 'y^2=12*x^6+24*x^5+50*x^4+x^3+10*x^2+52*x+43', 'y^2=x^6+22*x^5+12*x^4+14*x^3+14*x^2+56*x+41', 'y^2=21*x^6+54*x^5+43*x^4+30*x^3+24*x^2+52*x+46', 'y^2=65*x^6+39*x^5+16*x^4+52*x^3+47*x^2+8*x+22', 'y^2=12*x^6+52*x^5+23*x^4+57*x^3+42*x^2+13*x+19', 'y^2=60*x^6+22*x^5+8*x^4+53*x^3+27*x^2+6*x+4', 'y^2=8*x^6+19*x^5+46*x^4+30*x^3+37*x^2+33*x+31', 'y^2=7*x^6+2*x^5+52*x^4+19*x^2+33*x+30', 'y^2=5*x^6+41*x^5+18*x^4+13*x^3+40*x^2+29*x+43', 'y^2=50*x^6+22*x^5+54*x^4+18*x^3+4*x^2+51*x+16', 'y^2=45*x^6+28*x^5+32*x^4+11*x^3+37*x^2+63*x+31', 'y^2=63*x^6+3*x^5+63*x^4+4*x^3+14*x^2+50*x+32', 'y^2=26*x^6+3*x^5+57*x^4+23*x^3+48*x^2+9*x+19', 'y^2=20*x^6+19*x^5+31*x^4+49*x^3+50*x^2+63*x+14', 'y^2=27*x^6+25*x^5+31*x^4+22*x^3+52*x^2+x+62', 'y^2=65*x^6+40*x^5+59*x^4+57*x^3+2*x^2+31*x+25', 'y^2=40*x^6+41*x^5+4*x^4+13*x^3+20*x^2+51*x+34', 'y^2=6*x^6+18*x^5+38*x^4+13*x^3+22*x^2+55*x+50', 'y^2=63*x^6+2*x^5+21*x^4+15*x^3+20*x^2+19*x+16', 'y^2=42*x^6+33*x^5+61*x^4+14*x^3+12*x^2+54*x+2', 'y^2=63*x^6+47*x^5+48*x^4+42*x^3+29*x^2+31*x+46', 'y^2=36*x^6+57*x^5+6*x^4+12*x^3+7*x^2+38*x+12', 'y^2=39*x^6+28*x^5+58*x^4+13*x^3+33*x^2+28*x+61', 'y^2=12*x^6+30*x^5+52*x^4+62*x^3+55*x^2+55*x+57', 'y^2=40*x^6+39*x^5+45*x^3+22*x^2+64*x+60', 'y^2=21*x^6+50*x^5+7*x^4+26*x^3+18*x^2+8*x+50', 'y^2=23*x^6+57*x^5+18*x^4+x^3+4*x+5', 'y^2=45*x^6+18*x^5+24*x^4+11*x^3+48*x^2+66*x+63', 'y^2=39*x^6+35*x^5+15*x^4+19*x^3+18*x^2+39', 'y^2=19*x^6+28*x^5+37*x^4+26*x^3+58*x^2+33*x+51', 'y^2=44*x^6+64*x^5+35*x^4+33*x^3+10*x^2+26*x+61', 'y^2=3*x^6+9*x^5+52*x^4+43*x^3+32*x^2+55*x+56', 'y^2=38*x^6+21*x^5+29*x^4+32*x^3+23*x^2+12*x+37', 'y^2=44*x^6+54*x^5+42*x^4+6*x^3+48*x^2+18*x+46', 'y^2=32*x^6+4*x^5+61*x^4+26*x^3+21*x^2+50*x+20', 'y^2=28*x^6+43*x^5+22*x^4+53*x^3+63*x^2+6*x+8', 'y^2=20*x^6+63*x^5+61*x^4+3*x^3+65*x^2+60*x+26', 'y^2=47*x^6+63*x^5+21*x^4+61*x^3+51*x^2+8*x+18', 'y^2=43*x^6+11*x^5+8*x^4+6*x^3+11*x^2+56*x+55', 'y^2=56*x^6+55*x^5+38*x^4+8*x^3+6*x^2+16*x+53', 'y^2=4*x^6+7*x^5+33*x^4+47*x^3+54*x^2+2*x+64', 'y^2=34*x^6+62*x^5+33*x^4+59*x^3+27*x^2+49*x+27', 'y^2=47*x^6+18*x^5+40*x^4+6*x^2+3*x+40', 'y^2=5*x^6+14*x^5+47*x^4+34*x^3+6*x^2+54*x+37', 'y^2=26*x^6+18*x^5+32*x^4+21*x^3+2*x^2+52*x+43', 'y^2=23*x^6+47*x^5+38*x^4+33*x^3+24*x^2+57*x+43', 'y^2=16*x^6+42*x^5+32*x^4+34*x^3+24*x^2+30*x+5', 'y^2=18*x^6+39*x^5+60*x^4+29*x^3+51*x^2+42*x+61', 'y^2=48*x^6+47*x^5+17*x^4+63*x^3+28*x^2+13*x+37', 'y^2=39*x^6+12*x^5+5*x^4+29*x^3+22*x^2+41*x+1', 'y^2=30*x^6+19*x^5+25*x^4+51*x^3+12*x^2+42*x+4', 'y^2=62*x^6+59*x^5+53*x^4+36*x^3+30*x^2+28*x+41', 'y^2=62*x^6+45*x^5+55*x^4+22*x^3+65*x^2+44*x+60', 'y^2=18*x^6+51*x^5+48*x^4+34*x^3+5*x^2+2*x+23', 'y^2=11*x^6+65*x^5+46*x^4+41*x^3+57*x^2+6*x+30', 'y^2=6*x^6+16*x^5+56*x^4+13*x^3+3*x^2+8*x+58', 'y^2=52*x^6+25*x^5+59*x^4+29*x^3+37*x^2+61', 'y^2=51*x^6+45*x^5+6*x^4+32*x^3+26*x^2+6*x+12', 'y^2=40*x^6+50*x^5+33*x^4+10*x^3+52*x^2+15*x+34', 'y^2=41*x^6+10*x^5+30*x^4+7*x^3+35*x^2+5*x+44', 'y^2=42*x^6+16*x^5+16*x^4+33*x^3+46*x^2+65*x+38', 'y^2=33*x^6+54*x^5+13*x^4+48*x^3+46*x^2+19*x+53', 'y^2=61*x^6+62*x^5+31*x^4+7*x^3+17*x^2+43*x+66', 'y^2=10*x^6+54*x^5+37*x^4+23*x^3+61*x^2+23*x+12', 'y^2=41*x^6+24*x^5+45*x^4+65*x^3+57*x^2+32*x+46', 'y^2=27*x^6+60*x^5+58*x^4+47*x^3+7*x^2+29*x+7', 'y^2=8*x^6+11*x^5+45*x^4+25*x^3+63*x^2+22*x+37', 'y^2=29*x^6+x^5+49*x^4+53*x^3+7*x^2+52*x+39', 'y^2=58*x^6+61*x^5+47*x^4+61*x^2+17*x+42', 'y^2=11*x^6+51*x^5+63*x^3+21*x^2+53*x+7', 'y^2=14*x^6+31*x^5+21*x^4+30*x^3+23*x^2+46*x+43', 'y^2=28*x^6+14*x^5+3*x^4+65*x^3+45*x^2+30*x+36', 'y^2=8*x^6+26*x^5+40*x^4+25*x^3+29*x^2+18*x+23', 'y^2=23*x^6+17*x^5+53*x^4+41*x^3+22*x^2+26*x+58', 'y^2=3*x^6+57*x^5+40*x^4+22*x^3+49*x^2+14*x+8', 'y^2=42*x^6+35*x^5+48*x^4+58*x^3+60*x^2+25*x+44', 'y^2=6*x^6+31*x^5+44*x^4+30*x^3+20*x^2+3*x+37', 'y^2=50*x^6+7*x^5+43*x^4+55*x^3+34*x^2+33*x+36', 'y^2=12*x^6+56*x^5+58*x^4+15*x^3+6*x^2+20*x+44', 'y^2=28*x^6+36*x^5+5*x^4+42*x^3+35*x^2+57*x+64', 'y^2=23*x^6+29*x^5+15*x^4+46*x^3+6*x^2+13*x+46', 'y^2=6*x^6+34*x^5+7*x^4+8*x^3+14*x^2+44*x+56', 'y^2=56*x^6+61*x^5+55*x^4+66*x^3+39*x^2+10*x+15', 'y^2=39*x^6+63*x^5+8*x^4+9*x^3+33*x^2+65*x+30', 'y^2=21*x^6+14*x^5+39*x^4+12*x^3+27*x^2+55*x+20', 'y^2=3*x^6+63*x^5+8*x^4+6*x^3+11*x^2+46*x+62', 'y^2=54*x^6+5*x^5+2*x^4+28*x^3+42*x^2+32*x+22', 'y^2=19*x^6+59*x^5+64*x^4+49*x^3+64*x^2+49*x+54', 'y^2=46*x^6+3*x^5+3*x^4+60*x^3+32*x^2+48*x+3', 'y^2=44*x^6+24*x^5+37*x^4+28*x^3+29*x^2+33*x+7', 'y^2=38*x^6+34*x^5+38*x^4+54*x^3+25*x^2+25*x+58', 'y^2=8*x^6+64*x^5+56*x^4+28*x^2+44*x+54', 'y^2=26*x^6+64*x^5+17*x^4+37*x^3+47*x^2+15*x+9', 'y^2=56*x^6+46*x^5+26*x^4+9*x^3+37*x^2+39*x+36', 'y^2=49*x^6+33*x^5+23*x^4+45*x^3+28*x^2+27*x+28', 'y^2=44*x^6+45*x^5+19*x^4+46*x^3+25*x^2+33*x+44', 'y^2=24*x^6+51*x^5+25*x^4+8*x^2+9*x+64', 'y^2=52*x^6+34*x^5+23*x^4+24*x^3+65*x^2+15*x+46', 'y^2=38*x^6+28*x^5+11*x^4+63*x^3+45*x^2+43*x+47', 'y^2=30*x^6+65*x^5+59*x^4+44*x^3+29*x^2+35*x+25', 'y^2=14*x^6+11*x^5+56*x^4+14*x^3+2*x^2+2*x+3', 'y^2=59*x^6+62*x^5+28*x^4+20*x^3+33*x^2+30*x+47', 'y^2=23*x^6+22*x^5+43*x^4+7*x^3+60*x^2+25*x+32', 'y^2=7*x^6+12*x^5+39*x^4+40*x^3+66*x^2+13*x+14', 'y^2=48*x^6+33*x^5+22*x^4+29*x^3+24*x^2+63*x+13', 'y^2=41*x^6+3*x^5+58*x^4+39*x^3+3*x^2+54*x+65', 'y^2=40*x^6+49*x^5+66*x^4+20*x^3+46*x^2+32*x+3', 'y^2=25*x^6+21*x^5+49*x^4+57*x^3+64*x^2+42*x+5', 'y^2=7*x^6+31*x^5+18*x^4+30*x^3+38*x^2+64*x+15', 'y^2=53*x^6+63*x^5+38*x^3+52*x^2+16*x+21', 'y^2=3*x^6+48*x^5+58*x^4+26*x^3+56*x^2+45*x+27', 'y^2=62*x^6+10*x^5+22*x^4+32*x^3+40*x^2+41*x+13', 'y^2=34*x^6+3*x^5+62*x^4+42*x^3+50*x^2+27*x+15', 'y^2=56*x^6+45*x^5+59*x^4+9*x^3+6*x^2+31*x+34'], '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': ['4.0.162194025.1'], 'geometric_splitting_field': '4.0.162194025.1', 'geometric_splitting_polynomials': [[1424, -84, 85, -2, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 136, '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': 136, 'label': '2.67.ai_cn', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['4.0.162194025.1'], 'p': 67, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -8, 65, -536, 4489], 'poly_str': '1 -8 65 -536 4489 ', 'primitive_models': [], 'q': 67, 'real_poly': [1, -8, -69], 'simple_distinct': ['2.67.ai_cn'], 'simple_factors': ['2.67.ai_cnA'], 'simple_multiplicities': [1], 'singular_primes': ['2,-F^2+6*F+5*V-40'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.162194025.1', 'splitting_polynomials': [[1424, -84, 85, -2, 1]], 'twist_count': 2, 'twists': [['2.67.i_cn', '2.4489.co_gvz', 2]], 'weak_equivalence_count': 2, 'zfv_index': 4, 'zfv_index_factorization': [[2, 2]], 'zfv_is_bass': True, 'zfv_is_maximal': False, 'zfv_plus_index': 2, 'zfv_plus_index_factorization': [[2, 1]], 'zfv_plus_norm': 22449, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,-F^2+6*F+5*V-40']}
  • av_fq_endalg_factors • Show schema
    {'base_label': '2.67.ai_cn', 'extension_degree': 1, 'extension_label': '2.67.ai_cn', 'multiplicity': 1}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '4.0.162194025.1', 'center_dim': 4, 'divalg_dim': 1, 'extension_label': '2.67.ai_cn', 'galois_group': '4T3', 'places': [['15', '5', '66', '0'], ['48', '3', '1', '0']]}