Formats: - HTML - YAML - JSON - 2026-10-06T04:09:27.273760
  • av_fq_isog • Show schema
    {'abvar_count': 5467, 'abvar_counts': [5467, 20965945, 89961540592, 406058044617225, 1822939569867289027, 8182692208221819608320, 36732220463972109804532651, 164890958092451820762694986825, 740195515036879987908113763889648, 3322737664785206218293247569148309225], 'abvar_counts_str': '5467 20965945 89961540592 406058044617225 1822939569867289027 8182692208221819608320 36732220463972109804532651 164890958092451820762694986825 740195515036879987908113763889648 3322737664785206218293247569148309225 ', 'all_polarized_product': False, 'all_unpolarized_product': False, 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.558663130524899, 0.685281783202145], 'center_dim': 4, 'cohen_macaulay_max': 1, 'curve_count': 80, 'curve_counts': [80, 4668, 299108, 20150644, 1350200480, 90458087046, 6060710830016, 406067675921956, 27206534439670556, 1822837806242597868], 'curve_counts_str': '80 4668 299108 20150644 1350200480 90458087046 6060710830016 406067675921956 27206534439670556 1822837806242597868 ', 'curves': ['y^2=14*x^6+38*x^5+11*x^4+22*x^3+32*x^2+63*x+22', 'y^2=24*x^6+24*x^5+42*x^4+10*x^3+38*x^2+16*x+40', 'y^2=22*x^6+66*x^5+40*x^4+60*x^3+56*x^2+24*x+53', 'y^2=52*x^6+52*x^5+32*x^4+19*x^3+37*x^2+28*x+51', 'y^2=64*x^6+61*x^5+12*x^4+45*x^3+55*x^2+32*x+59', 'y^2=22*x^6+11*x^5+31*x^4+23*x^3+28*x^2+5*x+22', 'y^2=33*x^6+27*x^5+17*x^4+45*x^2+20*x+8', 'y^2=57*x^6+25*x^5+20*x^4+45*x^3+44*x^2+62', 'y^2=33*x^6+60*x^5+59*x^4+42*x^3+31*x^2+41*x+35', 'y^2=9*x^6+60*x^5+54*x^4+53*x^3+15*x^2+57*x+44', 'y^2=20*x^6+15*x^5+28*x^4+16*x^3+41*x^2+29*x+63', 'y^2=56*x^6+32*x^5+19*x^4+10*x^3+36*x^2+18*x+38', 'y^2=40*x^6+66*x^5+44*x^4+40*x^3+2*x^2+7*x+11', 'y^2=23*x^6+9*x^5+21*x^4+58*x^3+59*x^2+56*x+10', 'y^2=57*x^6+4*x^4+58*x^3+56*x^2+30', 'y^2=22*x^6+32*x^5+45*x^4+39*x^3+41*x^2+3*x+9', 'y^2=5*x^6+14*x^5+44*x^4+64*x^3+53*x^2+13*x+26', 'y^2=60*x^6+58*x^5+61*x^4+46*x^3+33*x^2+62*x+36', 'y^2=11*x^6+64*x^5+38*x^4+14*x^3+32*x^2+22*x+12', 'y^2=56*x^6+23*x^5+53*x^4+4*x^3+37*x^2+60*x+63', 'y^2=25*x^6+21*x^5+x^4+17*x^3+25*x^2+66*x+9', 'y^2=46*x^6+11*x^5+39*x^4+7*x^3+47*x^2+48*x+32', 'y^2=65*x^6+11*x^5+64*x^4+45*x^3+56*x^2+66*x+23', 'y^2=31*x^6+33*x^5+62*x^4+65*x^3+24*x^2+8*x+40', 'y^2=43*x^6+60*x^5+33*x^4+18*x^3+58*x^2+39*x+46', 'y^2=43*x^6+43*x^5+24*x^4+32*x^3+53*x^2+21*x+56', 'y^2=34*x^6+45*x^5+35*x^4+x^3+66*x^2+4*x+34', 'y^2=35*x^6+59*x^5+58*x^4+45*x^3+46*x^2+65*x+63', 'y^2=9*x^6+61*x^5+30*x^4+43*x^3+43*x^2+12*x+36', 'y^2=44*x^6+63*x^5+34*x^4+65*x^3+66*x^2+51*x+50', 'y^2=60*x^6+9*x^5+23*x^4+57*x^3+21*x^2+36*x+56', 'y^2=52*x^6+27*x^5+11*x^4+34*x^3+60*x^2+17*x+63', 'y^2=38*x^6+26*x^5+49*x^4+23*x^3+20*x^2+4*x+36', 'y^2=24*x^6+57*x^5+25*x^4+40*x^3+45*x^2+45*x+26', 'y^2=21*x^6+38*x^5+66*x^4+2*x^3+14*x^2+47*x+32', 'y^2=59*x^6+5*x^5+58*x^4+50*x^3+30*x^2+36*x+22', 'y^2=9*x^6+19*x^5+36*x^4+56*x^3+14*x^2+8', 'y^2=40*x^6+47*x^5+66*x^4+12*x^3+13*x^2+37*x+24', 'y^2=24*x^6+55*x^5+59*x^4+35*x^3+41*x^2+6*x+28', 'y^2=42*x^6+42*x^5+36*x^4+54*x^3+31*x^2+3*x+11', 'y^2=59*x^6+12*x^5+5*x^4+7*x^3+x^2+29*x+56', 'y^2=42*x^6+42*x^5+4*x^4+35*x^3+3*x^2+38*x+28', 'y^2=49*x^6+26*x^5+44*x^4+34*x^3+51*x^2+47*x+19', 'y^2=62*x^6+66*x^5+4*x^4+23*x^3+45*x^2+45*x+5', 'y^2=58*x^6+64*x^4+44*x^3+11*x^2+9*x+65', 'y^2=29*x^6+7*x^5+4*x^4+54*x^3+10*x^2+29*x+52', 'y^2=42*x^6+43*x^5+48*x^4+45*x^3+49*x^2+45*x+22', 'y^2=14*x^6+24*x^5+18*x^4+62*x^3+59*x^2+59*x+4', 'y^2=9*x^6+29*x^5+10*x^4+66*x^2+26*x+20', 'y^2=6*x^6+43*x^5+6*x^4+64*x^3+47*x^2+30*x+9', 'y^2=52*x^6+35*x^5+19*x^4+47*x^3+55*x^2+x+33', 'y^2=47*x^6+45*x^5+59*x^4+48*x^3+23*x^2+38*x+56', 'y^2=16*x^6+37*x^5+37*x^4+10*x^3+43*x^2+23*x+62', 'y^2=36*x^6+56*x^5+28*x^4+30*x^3+53*x^2+14*x+29', 'y^2=16*x^6+14*x^5+19*x^4+14*x^3+46*x^2+32*x+43', 'y^2=14*x^6+4*x^5+38*x^4+66*x^3+48*x^2+58*x+61', 'y^2=6*x^6+44*x^5+50*x^4+40*x^3+27*x^2+53*x+16', 'y^2=12*x^6+55*x^5+23*x^4+59*x^3+40*x^2+46*x+21', 'y^2=63*x^6+64*x^5+66*x^4+23*x^3+45*x^2+56*x+34', 'y^2=64*x^6+27*x^5+51*x^4+41*x^3+30*x^2+52*x+22', 'y^2=41*x^6+25*x^5+32*x^4+50*x^3+40*x^2+46*x+55', 'y^2=12*x^6+12*x^5+9*x^4+66*x^3+22*x^2+39*x+13', 'y^2=25*x^6+53*x^5+5*x^4+22*x^3+7*x^2+61*x+15', 'y^2=58*x^6+4*x^5+65*x^4+58*x^3+14*x^2+62*x+5', 'y^2=4*x^6+15*x^5+19*x^4+43*x^3+36*x^2+41*x+22', 'y^2=54*x^6+2*x^5+46*x^4+56*x^3+13*x^2+34*x+8', 'y^2=31*x^6+3*x^5+56*x^4+61*x^3+49*x^2+26*x+23', 'y^2=22*x^6+40*x^5+14*x^4+39*x^3+34*x^2+9*x+7', 'y^2=31*x^6+36*x^5+31*x^4+2*x^3+62*x^2+2*x+54', 'y^2=3*x^6+9*x^5+49*x^4+53*x^3+27*x^2+53*x+65', 'y^2=29*x^6+38*x^5+35*x^4+53*x^3+15*x^2+48*x+56', 'y^2=62*x^6+27*x^5+13*x^4+8*x^3+32*x^2+7*x+64', 'y^2=66*x^6+42*x^5+19*x^4+6*x^3+18*x^2+29*x+65', 'y^2=4*x^6+39*x^5+44*x^4+5*x^3+23*x^2+59*x+59', 'y^2=42*x^6+59*x^5+6*x^4+32*x^3+44*x^2+44*x+26', 'y^2=49*x^6+38*x^5+47*x^4+19*x^3+19*x^2+4*x+64', 'y^2=42*x^6+45*x^5+50*x^4+43*x^3+61*x^2+39*x+35', 'y^2=63*x^6+21*x^5+9*x^4+60*x^3+22*x^2+56*x+31', 'y^2=52*x^6+61*x^5+64*x^3+13*x+3', 'y^2=64*x^6+49*x^5+51*x^4+34*x^2+51*x+47', 'y^2=53*x^6+38*x^5+45*x^4+33*x^3+7*x^2+8*x+58', 'y^2=66*x^6+34*x^4+61*x^2+47*x+41', 'y^2=33*x^6+17*x^5+32*x^4+48*x^3+44*x^2+52*x+15', 'y^2=5*x^6+4*x^5+54*x^4+20*x^3+61*x^2+55*x+18', 'y^2=17*x^6+5*x^5+46*x^4+14*x^3+63*x^2+53*x+61', 'y^2=43*x^6+38*x^5+38*x^4+61*x^3+27*x^2+48*x+27', 'y^2=14*x^6+7*x^5+55*x^4+30*x^3+49*x^2+66*x+64', 'y^2=33*x^6+8*x^5+48*x^4+4*x^3+53*x^2+50*x+55'], 'dim1_distinct': 2, 'dim1_factors': 2, 'dim2_distinct': 0, 'dim2_factors': 0, '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': ['2T1', '2T1'], 'geom_dim1_distinct': 2, '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': 4, 'geometric_extension_degree': 1, 'geometric_galois_groups': ['2T1', '2T1'], 'geometric_number_fields': ['2.0.259.1', '2.0.187.1'], 'geometric_splitting_polynomials': [[324, 0, 223, 0, 1]], 'group_structure_count': 1, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 88, 'is_cyclic': True, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 88, 'label': '2.67.m_gf', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 2, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [], 'number_fields': ['2.0.259.1', '2.0.187.1'], 'p': 67, 'p_rank': 2, 'p_rank_deficit': 0, 'pic_prime_gens': [[1, 5, 1, 12], [1, 7, 1, 2], [2, 7, 1, 12], [1, 11, 1, 12]], 'poly': [1, 12, 161, 804, 4489], 'poly_str': '1 12 161 804 4489 ', 'primitive_models': [], 'principal_polarization_count': 96, 'q': 67, 'real_poly': [1, 12, 27], 'simple_distinct': ['1.67.d', '1.67.j'], 'simple_factors': ['1.67.dA', '1.67.jA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,-F^2-V-92', '3,-F^2-28*F-V-97'], 'size': 160, 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_polynomials': [[324, 0, 223, 0, 1]], 'twist_count': 4, 'twists': [['2.67.am_gf', '2.4489.gw_xcd', 2], ['2.67.ag_ed', '2.4489.gw_xcd', 2], ['2.67.g_ed', '2.4489.gw_xcd', 2]], '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': 96, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 48433, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,-F^2-V-92', '3,-F^2-28*F-V-97']}
  • av_fq_endalg_factors • Show schema
    • id: 68600
      {'base_label': '2.67.m_gf', 'extension_degree': 1, 'extension_label': '1.67.d', 'multiplicity': 1}
    • id: 68601
      {'base_label': '2.67.m_gf', 'extension_degree': 1, 'extension_label': '1.67.j', 'multiplicity': 1}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.259.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.67.d', 'galois_group': '2T1', 'places': [['1', '1'], ['65', '1']]}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.187.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.67.j', 'galois_group': '2T1', 'places': [['4', '1'], ['62', '1']]}