Formats: - HTML - YAML - JSON - 2026-10-07T07:58:01.694213
  • av_fq_isog • Show schema
    {'abvar_count': 816, 'abvar_counts': [816, 763776, 595321776, 501037056000, 420848335573296, 353769141462662016, 297552348838606002096, 250247167621141856256000, 210457344375999128235579696, 176994578616413359896783801216], 'abvar_counts_str': '816 763776 595321776 501037056000 420848335573296 353769141462662016 297552348838606002096 250247167621141856256000 210457344375999128235579696 176994578616413359896783801216 ', 'angle_corank': 0, 'angle_rank': 2, 'angles': [0.311919362152108, 0.621118941590843], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 28, 'curve_counts': [28, 906, 24412, 708398, 20518028, 594746586, 17249535212, 500247800158, 14507150112508, 420707239160106], 'curve_counts_str': '28 906 24412 708398 20518028 594746586 17249535212 500247800158 14507150112508 420707239160106 ', 'curves': ['y^2=22*x^6+x^5+8*x^4+8*x^3+12*x^2+25*x+11', 'y^2=2*x^6+11*x^5+22*x^4+11*x^3+10*x^2+2*x', 'y^2=5*x^5+20*x^4+24*x^3+17*x^2+28*x+5', 'y^2=5*x^6+4*x^5+11*x^4+7*x^3+19*x^2+3*x+24', 'y^2=20*x^6+15*x^5+28*x^4+18*x^3+5*x^2+28*x+11', 'y^2=24*x^6+22*x^5+22*x^4+11*x^3+20*x^2+25*x+4', 'y^2=15*x^6+19*x^5+14*x^4+18*x^3+27*x^2+24*x+11', 'y^2=26*x^6+7*x^5+25*x^4+6*x^3+12*x^2+22*x+8', 'y^2=20*x^6+11*x^5+24*x^3+11*x+20', 'y^2=11*x^6+10*x^5+12*x^4+15*x^3+12*x^2+10*x+11', 'y^2=15*x^6+15*x^5+22*x^4+8*x^3+2*x^2+28*x+9', 'y^2=9*x^6+23*x^5+16*x^4+3*x^3+16*x^2+23*x+9', 'y^2=15*x^6+7*x^5+20*x^4+12*x^3+x^2+13*x+19', 'y^2=9*x^6+7*x^5+21*x^3+2*x^2+11*x+6', 'y^2=24*x^6+5*x^5+7*x^3+6*x+7', 'y^2=17*x^6+10*x^5+22*x^4+11*x^3+21*x^2+7*x+21', 'y^2=18*x^6+5*x^5+3*x^4+7*x^3+2*x^2+28*x+15', 'y^2=16*x^6+23*x^5+9*x^4+15*x^3+23*x^2+5*x+2', 'y^2=3*x^6+9*x^5+11*x^4+24*x^3+16*x^2+14*x+6', 'y^2=15*x^6+5*x^5+15*x^4+13*x^3+11*x+13', 'y^2=7*x^6+3*x^5+16*x^4+14*x^3+27*x^2+18*x+2', 'y^2=18*x^6+14*x^5+24*x^3+7*x^2+27*x+22', 'y^2=13*x^6+20*x^5+2*x^4+21*x^3+23*x^2+7*x', 'y^2=3*x^6+2*x^5+14*x^4+26*x^3+10*x^2+4*x+6', 'y^2=12*x^6+20*x^5+14*x^4+14*x^2+20*x+12', 'y^2=16*x^6+5*x^5+25*x^3+28*x^2+11*x+14', 'y^2=15*x^6+23*x^5+15*x^4+18*x^3+9*x^2+25*x+27', 'y^2=4*x^6+10*x^5+x^4+17*x^3+21*x^2+11*x+17', 'y^2=8*x^6+18*x^5+2*x^4+20*x^3+8*x^2+4*x+24', 'y^2=12*x^6+12*x^5+16*x^4+11*x^2+24*x+2', 'y^2=4*x^6+4*x^5+9*x^4+25*x^3+21*x^2+23*x', 'y^2=10*x^6+24*x^4+23*x^3+13*x^2+6*x', 'y^2=19*x^6+28*x^5+23*x^4+18*x^3+25*x^2+22*x+27', 'y^2=16*x^6+18*x^4+11*x^3+17*x^2+28*x+25', 'y^2=14*x^6+22*x^5+26*x^4+6*x^2+x+11', 'y^2=9*x^6+16*x^5+15*x^4+17*x^3+24*x^2+19*x+6', 'y^2=4*x^6+20*x^5+23*x^4+16*x^3+5*x^2+8*x+4', 'y^2=9*x^6+16*x^5+13*x^4+25*x^3+26*x^2+17*x+11', 'y^2=7*x^6+10*x^5+12*x^4+15*x^3+7*x^2+x+16', 'y^2=13*x^6+14*x^4+27*x^3+25*x^2+18*x+27', 'y^2=20*x^6+2*x^5+11*x^4+x^3+4*x^2+8*x+24', 'y^2=19*x^6+26*x^5+2*x^4+8*x^3+13*x^2+21*x+24', 'y^2=8*x^6+22*x^5+18*x^4+18*x^3+16*x^2+24*x+3', 'y^2=8*x^6+24*x^5+23*x^4+8*x^3+2*x^2+20', 'y^2=25*x^6+16*x^5+13*x^4+21*x^3+15*x^2+13*x+4', 'y^2=11*x^6+8*x^5+2*x^4+25*x^3+9*x^2+21*x+6', 'y^2=10*x^6+16*x^5+9*x^4+25*x^3+18*x^2+26*x+27', 'y^2=19*x^6+6*x^5+4*x^4+14*x^3+4*x^2+6*x+12', 'y^2=6*x^6+25*x^5+8*x^3+25*x+6', 'y^2=17*x^6+9*x^5+8*x^4+23*x^3+22*x^2+25*x+6', 'y^2=4*x^6+11*x^5+14*x^4+8*x^3+14*x^2+11*x+4', 'y^2=25*x^6+19*x^5+22*x^4+9*x^3+25*x^2+3*x+5', 'y^2=9*x^6+23*x^5+22*x^4+15*x^3+9*x^2+14*x+12', 'y^2=3*x^6+21*x^5+23*x^4+22*x^3+24*x^2+10*x+13', 'y^2=3*x^6+8*x^5+15*x^4+16*x^3+15*x^2+8*x+3', 'y^2=9*x^6+23*x^5+19*x^4+4*x^3+14*x^2+3*x+2', 'y^2=4*x^6+24*x^5+5*x^4+17*x^3+5*x^2+24*x+4', 'y^2=4*x^5+4*x^4+5*x^3+4*x^2+22*x+21', 'y^2=11*x^6+10*x^5+10*x^4+6*x^3+12*x^2+26*x+3', 'y^2=12*x^6+23*x^5+20*x^4+13*x^3+3*x^2+16*x+19', 'y^2=9*x^6+13*x^5+23*x^4+5*x^3+23*x^2+13*x+9', 'y^2=15*x^6+9*x^5+25*x^4+9*x^3+6*x^2+19*x+2', 'y^2=5*x^6+24*x^5+x^4+27*x^3+4*x^2+8', 'y^2=20*x^6+12*x^5+13*x^4+15*x^3+25*x^2+8*x+13', 'y^2=22*x^6+16*x^5+9*x^4+15*x^3+9*x^2+16*x+22', 'y^2=27*x^6+x^5+24*x^4+14*x^3+18*x^2+21*x+28', 'y^2=5*x^6+25*x^5+5*x^4+3*x^3+5*x^2+25*x+5', 'y^2=25*x^6+24*x^5+3*x^4+5*x^3+8*x^2+14*x+28', 'y^2=22*x^6+26*x^5+19*x^4+20*x^3+2*x^2+13*x+4', 'y^2=9*x^6+20*x^5+15*x^4+28*x^3+13*x^2+17*x+28', 'y^2=8*x^6+25*x^5+16*x^4+22*x^3+2*x^2+22*x+26', 'y^2=2*x^6+21*x^5+25*x^4+13*x^3+18*x^2+3*x+9', 'y^2=18*x^6+6*x^5+26*x^4+28*x^3+26*x^2+6*x+18', 'y^2=26*x^6+3*x^5+25*x^4+8*x^3+23*x^2+20*x+2', 'y^2=18*x^6+7*x^5+8*x^4+24*x^3+x^2+23*x+26', 'y^2=26*x^6+16*x^5+16*x^4+16*x^3+24*x^2+8*x+3', 'y^2=16*x^6+14*x^5+25*x^4+x^3+x^2+19*x+7', 'y^2=21*x^6+19*x^5+5*x^4+10*x^3+10*x^2+4*x+18', 'y^2=2*x^6+21*x^5+x^4+24*x^3+5*x^2+3*x+18', 'y^2=21*x^6+18*x^5+27*x^4+22*x^3+17*x^2+15*x+11', 'y^2=9*x^6+15*x^5+9*x^4+4*x^3+8*x^2+15*x+11', 'y^2=27*x^6+23*x^5+9*x^4+17*x^3+9*x^2+23*x+27', 'y^2=x^5+17*x^4+23*x^3+2*x^2+20*x+1', 'y^2=10*x^6+27*x^5+2*x^4+17*x^3+11*x^2+25*x+16', 'y^2=19*x^6+17*x^5+10*x^4+12*x^3+3*x^2+14*x+18', 'y^2=7*x^6+25*x^5+8*x^4+4*x^3+15*x', 'y^2=4*x^6+3*x^5+15*x^4+7*x^3+6*x^2+18*x+10', 'y^2=3*x^6+15*x^5+24*x^4+24*x^3+19*x^2+4*x+18', 'y^2=19*x^6+2*x^5+4*x^4+7*x^3+3*x^2+16*x+2', 'y^2=9*x^6+27*x^5+21*x^4+6*x^3+9*x+2'], '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': 30, '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': ['2.0.20.1', '2.0.4.1'], 'geometric_splitting_field': '4.0.400.1', 'geometric_splitting_polynomials': [[1, 0, 3, 0, 1]], 'group_structure_count': 4, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 90, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 90, 'label': '2.29.ac_bi', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 4, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['2.0.20.1', '2.0.4.1'], 'p': 29, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, -2, 34, -58, 841], 'poly_str': '1 -2 34 -58 841 ', 'primitive_models': [], 'q': 29, 'real_poly': [1, -2, -24], 'simple_distinct': ['1.29.ag', '1.29.e'], 'simple_factors': ['1.29.agA', '1.29.eA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,7*F-9', '5,4*F-7*V+4'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '4.0.400.1', 'splitting_polynomials': [[1, 0, 3, 0, 1]], 'twist_count': 8, 'twists': [['2.29.ak_de', '2.841.cm_dwg', 2], ['2.29.c_bi', '2.841.cm_dwg', 2], ['2.29.k_de', '2.841.cm_dwg', 2], ['2.29.aq_eo', '2.707281.bqy_cwxfy', 4], ['2.29.ae_ac', '2.707281.bqy_cwxfy', 4], ['2.29.e_ac', '2.707281.bqy_cwxfy', 4], ['2.29.q_eo', '2.707281.bqy_cwxfy', 4]], 'weak_equivalence_count': 42, 'zfv_index': 1000, 'zfv_index_factorization': [[2, 3], [5, 3]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 8000, 'zfv_singular_count': 4, 'zfv_singular_primes': ['2,7*F-9', '5,4*F-7*V+4']}
  • av_fq_endalg_factors • Show schema
    • id: 19452
      {'base_label': '2.29.ac_bi', 'extension_degree': 1, 'extension_label': '1.29.ag', 'multiplicity': 1}
    • id: 19453
      {'base_label': '2.29.ac_bi', 'extension_degree': 1, 'extension_label': '1.29.e', 'multiplicity': 1}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.20.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.29.ag', 'galois_group': '2T1', 'places': [['13', '1'], ['16', '1']]}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.4.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.29.e', 'galois_group': '2T1', 'places': [['12', '1'], ['17', '1']]}