# Stored data for abelian variety isogeny class 1.19.ai, downloaded from the LMFDB on 17 November 2025.
{"abvar_count": 12, "abvar_counts": [12, 336, 6804, 130368, 2477532, 47056464, 893929188, 16983821568, 322688674476, 6131069159376], "abvar_counts_str": "12 336 6804 130368 2477532 47056464 893929188 16983821568 322688674476 6131069159376 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.130073469146503], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 12, "curve_counts": [12, 336, 6804, 130368, 2477532, 47056464, 893929188, 16983821568, 322688674476, 6131069159376], "curve_counts_str": "12 336 6804 130368 2477532 47056464 893929188 16983821568 322688674476 6131069159376 ", "curves": ["y^2=x^3+x+2", "y^2=x^3+1"], "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": 2, "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "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.ai", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.3.1"], "p": 19, "p_rank": 1, "p_rank_deficit": 0, "pic_prime_gens": [], "poly": [1, -8, 19], "poly_str": "1 -8 19 ", "primitive_models": [], "principal_polarization_count": 2, "q": 19, "real_poly": [1, -8], "simple_distinct": ["1.19.ai"], "simple_factors": ["1.19.aiA"], "simple_multiplicities": [1], "singular_primes": ["2,F-1"], "size": 2, "slopes": ["0A", "1A"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 6, "twists": [["1.19.i", "1.361.aba", 2], ["1.19.b", "1.6859.ace", 3], ["1.19.h", "1.6859.ace", 3], ["1.19.ah", "1.47045881.pra", 6], ["1.19.ab", "1.47045881.pra", 6]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 1, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 12, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F-1"]}