# Stored data for abelian variety isogeny class 1.19.f, downloaded from the LMFDB on 14 September 2026.
{"abvar_count": 25, "abvar_counts": [25, 375, 6700, 130875, 2476375, 47034000, 893925925, 16983517875, 322686894100, 6131071134375], "abvar_counts_str": "25 375 6700 130875 2476375 47034000 893925925 16983517875 322686894100 6131071134375 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.69443002753289], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 25, "curve_counts": [25, 375, 6700, 130875, 2476375, 47034000, 893925925, 16983517875, 322686894100, 6131071134375], "curve_counts_str": "25 375 6700 130875 2476375 47034000 893925925 16983517875 322686894100 6131071134375 ", "curves": ["y^2=x^3+10*x+1", "y^2=x^3+7*x+14"], "dim1_distinct": 1, "dim1_factors": 1, "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": 1, "g": 1, "galois_groups": ["2T1"], "geom_dim1_distinct": 1, "geom_dim1_factors": 1, "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": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.51.1"], "geometric_splitting_field": "2.0.51.1", "geometric_splitting_polynomials": [[13, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 2, "label": "1.19.f", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.51.1"], "p": 19, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, 5, 19], "poly_str": "1 5 19 ", "primitive_models": [], "principal_polarization_count": 2, "q": 19, "real_poly": [1, 5], "simple_distinct": ["1.19.f"], "simple_factors": ["1.19.fA"], "simple_multiplicities": [1], "singular_primes": [], "size": 2, "slopes": ["0A", "1A"], "splitting_field": "2.0.51.1", "splitting_polynomials": [[13, -1, 1]], "twist_count": 2, "twists": [["1.19.af", "1.361.n", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 51, "zfv_singular_count": 0, "zfv_singular_primes": []}