# Stored data for abelian variety isogeny class 2.59.ai_f, downloaded from the LMFDB on 21 January 2026.
{"abvar_count": 3007, "abvar_counts": [3007, 11928769, 41810434576, 146781415010425, 511101762492651727, 1779163129258415769856, 6193381199375557108638007, 21559176252312776857771374825, 75047493404593669644288090466576, 261240334998485220504197952859252129], "abvar_counts_str": "3007 11928769 41810434576 146781415010425 511101762492651727 1779163129258415769856 6193381199375557108638007 21559176252312776857771374825 75047493404593669644288090466576 261240334998485220504197952859252129 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.00768306809499537, 0.658983598571671], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 52, "curve_counts": [52, 3428, 203572, 12113316, 714903332, 42179720726, 2488649470268, 146830429739716, 8662995455104108, 511116752310449828], "curve_counts_str": "52 3428 203572 12113316 714903332 42179720726 2488649470268 146830429739716 8662995455104108 511116752310449828 ", "curves": ["y^2=7*x^6+34*x^5+50*x^4+3*x^3+45*x^2+10*x+3", "y^2=51*x^6+51*x^5+40*x^4+37*x^3+29*x^2+35*x+48", "y^2=47*x^6+x^5+45*x^4+43*x^3+54*x^2+6*x+36", "y^2=56*x^6+58*x^5+29*x^4+37*x^3+58*x^2+4*x+57", "y^2=45*x^6+22*x^5+28*x^4+54*x^3+37*x^2+43*x+3", "y^2=17*x^6+55*x^4+42*x^3+40*x^2+34*x+43", "y^2=30*x^6+48*x^5+14*x^4+44*x^3+57*x^2+44*x+41", "y^2=26*x^6+13*x^5+39*x^4+5*x^3+2*x^2+34*x+41"], "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": 4, "g": 2, "galois_groups": ["4T2"], "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.43.1"], "geometric_splitting_field": "2.0.43.1", "geometric_splitting_polynomials": [[11, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 8, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 8, "label": "2.59.ai_f", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.16641.1"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -8, 5, -472, 3481], "poly_str": "1 -8 5 -472 3481 ", "primitive_models": [], "q": 59, "real_poly": [1, -8, -113], "simple_distinct": ["2.59.ai_f"], "simple_factors": ["2.59.ai_fA"], "simple_multiplicities": [1], "singular_primes": ["2,2*F^2+F-V+5", "5,-F^2-F-V"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.16641.1", "splitting_polynomials": [[121, -11, -10, -1, 1]], "twist_count": 6, "twists": [["2.59.i_f", "2.3481.acc_avt", 2], ["2.59.q_ha", "2.205379.acro_crwnu", 3], ["2.59.aq_ha", "2.42180533641.abugoa_bfbxbxnfy", 6], ["2.59.a_cc", "2.42180533641.abugoa_bfbxbxnfy", 6], ["2.59.i_f", "2.42180533641.abugoa_bfbxbxnfy", 6], ["2.59.a_acc", "2.1779197418239532716881.audlaynoe_gamnsnstkykyzwqg", 12]], "weak_equivalence_count": 4, "zfv_index": 20, "zfv_index_factorization": [[2, 2], [5, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 25, "zfv_singular_count": 4, "zfv_singular_primes": ["2,2*F^2+F-V+5", "5,-F^2-F-V"]}