# Stored data for abelian variety isogeny class 2.19.a_abi, downloaded from the LMFDB on 14 January 2026.
{"abvar_count": 328, "abvar_counts": [328, 107584, 47043400, 16870892544, 6131069611528, 2213081483560000, 799006687561857928, 288443868954489667584, 104127350298246255238600, 37590014581402100830494784], "abvar_counts_str": "328 107584 47043400 16870892544 6131069611528 2213081483560000 799006687561857928 288443868954489667584 104127350298246255238600 37590014581402100830494784 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0736815333794714, 0.926318466620529], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 20, "curve_counts": [20, 294, 6860, 129454, 2476100, 47040918, 893871740, 16983707614, 322687697780, 6131072965254], "curve_counts_str": "20 294 6860 129454 2476100 47040918 893871740 16983707614 322687697780 6131072965254 ", "curves": ["y^2=12*x^6+9*x^5+17*x^4+7*x^3+8*x^2+18*x+16", "y^2=9*x^6+7*x^5+8*x^4+10*x^3+9*x^2+2*x+16", "y^2=14*x^6+6*x^5+14*x^4+14*x^3+15*x^2+10*x+3", "y^2=x^5+18*x", "y^2=5*x^5+18*x^4+12*x^2+2*x"], "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": 8, "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.8.1"], "geometric_splitting_field": "2.0.8.1", "geometric_splitting_polynomials": [[2, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 5, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 5, "label": "2.19.a_abi", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.256.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -34, 0, 361], "poly_str": "1 0 -34 0 361 ", "primitive_models": [], "q": 19, "real_poly": [1, 0, -72], "simple_distinct": ["2.19.a_abi"], "simple_factors": ["2.19.a_abiA"], "simple_multiplicities": [1], "singular_primes": ["2,3*F-2*V+5", "3,22*F-14*V-3"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.256.1", "splitting_polynomials": [[1, 0, 0, 0, 1]], "twist_count": 8, "twists": [["2.19.ae_bq", "2.130321.abhk_zofe", 4], ["2.19.a_bi", "2.130321.abhk_zofe", 4], ["2.19.e_bq", "2.130321.abhk_zofe", 4], ["2.19.am_cu", "2.16983563041.ifwm_ewwqrfbq", 8], ["2.19.m_cu", "2.16983563041.ifwm_ewwqrfbq", 8], ["2.19.ac_ap", "2.2213314919066161.ouvweu_didjdriiuvry", 12], ["2.19.c_ap", "2.2213314919066161.ouvweu_didjdriiuvry", 12]], "weak_equivalence_count": 10, "zfv_index": 72, "zfv_index_factorization": [[2, 3], [3, 2]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 6, "zfv_plus_index_factorization": [[2, 1], [3, 1]], "zfv_plus_norm": 16, "zfv_singular_count": 4, "zfv_singular_primes": ["2,3*F-2*V+5", "3,22*F-14*V-3"]}