# Stored data for abelian variety isogeny class 1.89.ai, downloaded from the LMFDB on 21 January 2026.
{"abvar_count": 82, "abvar_counts": [82, 8036, 706594, 62745088, 5583937682, 496980063524, 44231335913378, 3936588923086848, 350356404555974866, 31181719926306856676], "abvar_counts_str": "82 8036 706594 62745088 5583937682 496980063524 44231335913378 3936588923086848 350356404555974866 31181719926306856676 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.360625947618812], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 82, "curve_counts": [82, 8036, 706594, 62745088, 5583937682, 496980063524, 44231335913378, 3936588923086848, 350356404555974866, 31181719926306856676], "curve_counts_str": "82 8036 706594 62745088 5583937682 496980063524 44231335913378 3936588923086848 350356404555974866 31181719926306856676 ", "curves": ["y^2=x^3+12*x+36", "y^2=x^3+39*x+28", "y^2=x^3+47*x+47", "y^2=x^3+88*x+86"], "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": ["2.0.292.1"], "geometric_splitting_field": "2.0.292.1", "geometric_splitting_polynomials": [[73, 0, 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": 4, "label": "1.89.ai", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.292.1"], "p": 89, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -8, 89], "poly_str": "1 -8 89 ", "primitive_models": [], "principal_polarization_count": 4, "q": 89, "real_poly": [1, -8], "simple_distinct": ["1.89.ai"], "simple_factors": ["1.89.aiA"], "simple_multiplicities": [1], "singular_primes": [], "size": 4, "slopes": ["0A", "1A"], "splitting_field": "2.0.292.1", "splitting_polynomials": [[73, 0, 1]], "twist_count": 2, "twists": [["1.89.i", "1.7921.ek", 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": 292, "zfv_singular_count": 0, "zfv_singular_primes": []}