Formats: - HTML - YAML - JSON - 2026-07-17T09:30:04.678953
  • av_fq_isog • Show schema
    {'abvar_count': 1760, 'abvar_counts': [1760, 3097600, 4750185440, 7969554841600, 13422659310764000, 22564261714387993600, 37929227194687777430240, 63759002843475832740249600, 107178930967531162607229121760, 180167782972839499526263696000000], 'abvar_counts_str': '1760 3097600 4750185440 7969554841600 13422659310764000 22564261714387993600 37929227194687777430240 63759002843475832740249600 107178930967531162607229121760 180167782972839499526263696000000 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.450084017046191, 0.549915982953809], 'center_dim': 4, 'cohen_macaulay_max': 3, 'curve_count': 42, 'curve_counts': [42, 1838, 68922, 2820318, 115856202, 4750266638, 194754273882, 7984921713598, 327381934393962, 13422659311375598], 'curve_counts_str': '42 1838 68922 2820318 115856202 4750266638 194754273882 7984921713598 327381934393962 13422659311375598 ', 'curves': ['y^2=40*x^6+10*x^5+13*x^4+34*x^3+19*x^2+x+28', 'y^2=35*x^6+19*x^5+37*x^4+40*x^3+32*x^2+6*x+4', 'y^2=37*x^6+25*x^5+36*x^4+30*x^3+16*x^2+21*x+4', 'y^2=23*x^6+4*x^5+7*x^4+35*x^3+38*x^2+17*x+26', 'y^2=15*x^6+24*x^5+x^4+5*x^3+23*x^2+20*x+33', 'y^2=21*x^6+33*x^4+34*x^2+26', 'y^2=22*x^6+3*x^4+18*x^2+37', 'y^2=13*x^6+27*x^4+39*x^2+20', 'y^2=30*x^6+9*x^4+13*x^2+2', 'y^2=13*x^6+39*x^5+2*x^4+14*x^3+22*x^2+19*x+39', 'y^2=37*x^6+29*x^5+12*x^4+2*x^3+9*x^2+32*x+29', 'y^2=40*x^6+26*x^5+17*x^4+18*x^3+17*x^2+26*x+40', 'y^2=35*x^6+33*x^5+20*x^4+26*x^3+20*x^2+33*x+35', 'y^2=38*x^6+34*x^5+29*x^4+30*x^3+18*x^2+18*x+4', 'y^2=16*x^6+10*x^5+31*x^4+34*x^3+40*x^2+35*x+34', 'y^2=13*x^5+6*x^4+40*x^3+6*x^2+13*x', 'y^2=37*x^5+36*x^4+35*x^3+36*x^2+37*x', 'y^2=2*x^6+2*x^5+19*x^4+28*x^3+12*x^2+20*x+4', 'y^2=12*x^6+12*x^5+32*x^4+4*x^3+31*x^2+38*x+24', 'y^2=20*x^6+26*x^4+22*x^3+7*x^2+30*x+18', 'y^2=38*x^6+33*x^4+9*x^3+x^2+16*x+26', 'y^2=11*x^6+16*x^5+18*x^4+15*x^3+18*x^2+16*x+11', 'y^2=25*x^6+14*x^5+26*x^4+8*x^3+26*x^2+14*x+25', 'y^2=22*x^6+x^5+23*x^4+40*x^3+23*x^2+x+22', 'y^2=9*x^6+6*x^5+15*x^4+35*x^3+15*x^2+6*x+9', 'y^2=3*x^6+23*x^5+39*x^4+38*x^3+27*x^2+8*x+29', 'y^2=18*x^6+15*x^5+29*x^4+23*x^3+39*x^2+7*x+10', 'y^2=40*x^6+38*x^5+9*x^4+9*x^2+38*x+40', 'y^2=35*x^6+23*x^5+13*x^4+13*x^2+23*x+35', 'y^2=26*x^6+31*x^5+3*x^4+21*x^3+29*x^2+25*x+40', 'y^2=33*x^6+22*x^5+18*x^4+3*x^3+10*x^2+27*x+35', 'y^2=22*x^6+4*x^5+39*x^4+16*x^3+39*x^2+4*x+22', 'y^2=9*x^6+24*x^5+29*x^4+14*x^3+29*x^2+24*x+9', 'y^2=8*x^6+23*x^5+20*x^4+15*x^3+17*x^2+11', 'y^2=7*x^6+15*x^5+38*x^4+8*x^3+20*x^2+25', 'y^2=19*x^6+19*x^5+31*x^4+6*x^3+31*x^2+19*x+19', 'y^2=32*x^6+32*x^5+22*x^4+36*x^3+22*x^2+32*x+32', 'y^2=26*x^6+28*x^5+38*x^4+x^3+38*x^2+28*x+26', 'y^2=33*x^6+4*x^5+23*x^4+6*x^3+23*x^2+4*x+33', 'y^2=27*x^6+12*x^5+19*x^4+38*x^3+19*x^2+12*x+27', 'y^2=39*x^6+31*x^5+32*x^4+23*x^3+32*x^2+31*x+39', 'y^2=32*x^6+31*x^4+22*x^2+24', 'y^2=11*x^6+5*x^4+30*x^2+39', 'y^2=20*x^6+38*x^5+2*x^4+x^3+13*x^2+28*x+8', 'y^2=38*x^6+23*x^5+12*x^4+6*x^3+37*x^2+4*x+7', 'y^2=7*x^6+34*x^5+3*x^4+19*x^3+36*x^2+24*x+30', 'y^2=x^6+40*x^5+18*x^4+32*x^3+11*x^2+21*x+16', 'y^2=3*x^6+37*x^5+31*x^4+x^3+31*x^2+37*x+3', 'y^2=18*x^6+17*x^5+22*x^4+6*x^3+22*x^2+17*x+18', 'y^2=20*x^6+34*x^5+8*x^4+20*x^3+5*x^2+12*x+2', 'y^2=38*x^6+40*x^5+7*x^4+38*x^3+30*x^2+31*x+12', 'y^2=9*x^6+23*x^5+18*x^4+19*x^3+19*x^2+28*x+25', 'y^2=34*x^6+9*x^5+17*x^4+23*x^3+12*x^2+33*x+6', 'y^2=40*x^6+13*x^5+20*x^4+15*x^3+31*x^2+34*x+36', 'y^2=25*x^6+23*x^5+4*x^4+12*x^3+33*x^2+10*x+5', 'y^2=27*x^6+15*x^5+24*x^4+31*x^3+34*x^2+19*x+30', 'y^2=39*x^6+4*x^5+31*x^4+21*x^3+33*x^2+37*x+18', 'y^2=29*x^6+24*x^5+22*x^4+3*x^3+34*x^2+17*x+26', 'y^2=34*x^6+12*x^4+31*x^2+5', 'y^2=9*x^6+24*x^4+21*x^2+17', 'y^2=15*x^6+7*x^5+35*x^4+2*x^3+13*x^2+34*x+12', 'y^2=8*x^6+x^5+5*x^4+12*x^3+37*x^2+40*x+31', 'y^2=25*x^6+36*x^5+7*x^4+16*x^3+14*x^2+21*x+36', 'y^2=27*x^6+11*x^5+x^4+14*x^3+2*x^2+3*x+11', 'y^2=3*x^6+40*x^4+35*x^2+33', 'y^2=40*x^6+37*x^4+17*x^2+30', 'y^2=2*x^6+16*x^5+25*x^4+36*x^3+25*x^2+16*x+2', 'y^2=12*x^6+14*x^5+27*x^4+11*x^3+27*x^2+14*x+12', 'y^2=38*x^6+x^5+25*x^4+16*x^3+26*x^2+17*x+11', 'y^2=23*x^6+6*x^5+27*x^4+14*x^3+33*x^2+20*x+25', 'y^2=12*x^6+33*x^5+27*x^4+24*x^3+27*x^2+33*x+12', 'y^2=31*x^6+34*x^5+39*x^4+21*x^3+39*x^2+34*x+31', 'y^2=13*x^6+12*x^5+7*x^4+17*x^3+22*x^2+29*x+6', 'y^2=37*x^6+31*x^5+x^4+20*x^3+9*x^2+10*x+36', 'y^2=30*x^6+15*x^5+40*x^4+31*x^3+30*x^2+26*x+38', 'y^2=16*x^6+8*x^5+35*x^4+22*x^3+16*x^2+33*x+23', 'y^2=29*x^6+14*x^5+15*x^4+32*x^3+15*x^2+14*x+29', 'y^2=10*x^6+2*x^5+8*x^4+28*x^3+8*x^2+2*x+10'], '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': 14, 'g': 2, 'galois_groups': ['2T1', '2T1'], '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': ['2.0.40.1'], 'geometric_splitting_field': '2.0.40.1', 'geometric_splitting_polynomials': [[10, 0, 1]], 'group_structure_count': 6, 'has_geom_ss_factor': False, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 78, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 78, 'label': '2.41.a_da', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 1, 'max_twist_degree': 6, 'newton_coelevation': 2, 'newton_elevation': 0, 'noncyclic_primes': [2], 'number_fields': ['2.0.40.1', '2.0.40.1'], 'p': 41, 'p_rank': 2, 'p_rank_deficit': 0, 'poly': [1, 0, 78, 0, 1681], 'poly_str': '1 0 78 0 1681 ', 'primitive_models': [], 'q': 41, 'real_poly': [1, 0, -4], 'simple_distinct': ['1.41.ac', '1.41.c'], 'simple_factors': ['1.41.acA', '1.41.cA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,5*F+1'], 'slopes': ['0A', '0B', '1A', '1B'], 'splitting_field': '2.0.40.1', 'splitting_polynomials': [[10, 0, 1]], 'twist_count': 6, 'twists': [['2.41.ae_di', '2.1681.ga_nzi', 2], ['2.41.e_di', '2.1681.ga_nzi', 2], ['2.41.a_ada', '2.2825761.aibk_bcpcss', 4], ['2.41.ac_abl', '2.4750104241.jgga_cacmzzvy', 6], ['2.41.c_abl', '2.4750104241.jgga_cacmzzvy', 6]], 'weak_equivalence_count': 23, 'zfv_index': 64, 'zfv_index_factorization': [[2, 6]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 25600, 'zfv_singular_count': 2, 'zfv_singular_primes': ['2,5*F+1']}
  • av_fq_endalg_factors • Show schema
    • id: 29770
      {'base_label': '2.41.a_da', 'extension_degree': 1, 'extension_label': '1.41.ac', 'multiplicity': 1}
    • id: 29771
      {'base_label': '2.41.a_da', 'extension_degree': 1, 'extension_label': '1.41.c', 'multiplicity': 1}
    • id: 29772
      {'base_label': '2.41.a_da', 'extension_degree': 2, 'extension_label': '1.1681.da', 'multiplicity': 2}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.40.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.41.ac', 'galois_group': '2T1', 'places': [['20', '1'], ['21', '1']]}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.40.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.41.c', 'galois_group': '2T1', 'places': [['21', '1'], ['20', '1']]}
  • av_fq_endalg_data • Show schema
    {'brauer_invariants': ['0', '0'], 'center': '2.0.40.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.1681.da', 'galois_group': '2T1', 'places': [['20', '1'], ['21', '1']]}