Formats: - HTML - YAML - JSON - 2026-10-24T15:33:31.832297
Query: /api/av_fq_isog/?_offset=0

Table av_fq_isog

Isogeny classes of abelian varieties over finite fields

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{'abvar_count': 8000, 'abvar_counts': [8000, 64000000, 322828856000, 2176782336000000, 15181145423081000000, 104218470266268736000000, 714209498090393265704024000, 4898537395446678479437824000000, 33600614943772830373610771098952000, 230467176356733194487532561000000000000], 'abvar_counts_str': '8000 64000000 322828856000 2176782336000000 15181145423081000000 104218470266268736000000 714209498090393265704024000 4898537395446678479437824000000 33600614943772830373610771098952000 230467176356733194487532561000000000000 ', 'angle_corank': 3, 'angle_rank': 0, 'angles': [0.5, 0.5, 0.5], 'center_dim': 2, 'curve_count': 20, 'curve_counts': [20, 476, 6860, 128156, 2476100, 47087036, 893871740, 16982781116, 322687697780, 6131081114396], 'curve_counts_str': '20 476 6860 128156 2476100 47087036 893871740 16982781116 322687697780 6131081114396 ', 'curves': ['y^2=x^7+18*x^6+17*x^5+9*x^4+13*x^3+10*x^2+8*x', 'y^2=x^7+14*x^6+16*x^5+4*x^3+11*x^2+11*x', 'y^2=x^7+4*x^5+15*x^3+18*x', 'y^2=x^7+17*x^5+5*x^3+3*x', 'y^2=x^8+x^7+2*x^6+3*x^5+13*x^4+16*x^3+2*x^2+18*x+1', 'y^2=18*x^8+18*x^7+17*x^6+16*x^5+6*x^4+3*x^3+17*x^2+x+18', 'y^2=x^8+5*x^6+14*x^2+18', 'y^2=x^7+11*x^5+12*x^3+6*x', 'y^2=x^8+14*x^6+5*x^2+18', 'y^2=x^7+15*x^5+15*x^3+x', 'y^2=x^8+11*x^7+14*x^6+5*x^2+11*x+18', 'y^2=x^8+13*x^7+15*x^6+4*x^5+9*x^4+15*x^3+15*x^2+6*x+1', 'y^2=x^8+18*x^7+18*x^6+11*x^5+8*x^4+13*x^3+5*x^2+x+17', 'y^2=18*x^8+x^7+x^6+8*x^5+11*x^4+6*x^3+14*x^2+18*x+2'], 'dim1_distinct': 1, 'dim1_factors': 3, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'g': 3, 'galois_groups': ['2T1'], 'geom_dim1_distinct': 1, 'geom_dim1_factors': 3, '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': 1, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['1T1'], 'geometric_number_fields': ['1.1.1.1'], 'geometric_splitting_field': '1.1.1.1', 'geometric_splitting_polynomials': [[0, 1]], 'has_geom_ss_factor': True, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 14, 'id': 1632770, 'is_cyclic': False, 'is_geometrically_simple': False, 'is_geometrically_squarefree': False, 'is_primitive': True, 'is_simple': False, 'is_squarefree': False, 'is_supersingular': True, 'label': '3.19.a_cf_a', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 12, 'newton_coelevation': 0, 'newton_elevation': 4, 'noncyclic_primes': [2, 5], 'number_fields': ['2.0.19.1'], 'p': 19, 'p_rank': 0, 'p_rank_deficit': 3, 'poly': [1, 0, 57, 0, 1083, 0, 6859], 'poly_str': '1 0 57 0 1083 0 6859 ', 'primitive_models': [], 'q': 19, 'real_poly': [1], 'simple_distinct': ['1.19.a'], 'simple_factors': ['1.19.aA', '1.19.aB', '1.19.aC'], 'simple_multiplicities': [3], 'slopes': ['1/2A', '1/2B', '1/2C', '1/2D', '1/2E', '1/2F'], 'splitting_field': '2.0.19.1', 'splitting_polynomials': [[5, -1, 1]], 'twist_count': 5, 'twists': [['3.19.a_a_a', '3.6859.a_bell_a', 3], ['3.19.a_at_a', '3.130321.adfi_ehftf_adbfafzg', 4], ['3.19.a_t_a', '3.16983563041.absmsc_bfsrkqrmt_amboxwpcwzoau', 8], ['3.19.a_bm_a', '3.2213314919066161.axtsgzu_jberxlirgeap_abvtqonhbgrckauarzg', 12]]}