# Stored data for abelian variety isogeny class 1.31.ae, downloaded from the LMFDB on 07 March 2026.
{"abvar_count": 28, "abvar_counts": [28, 1008, 30100, 923328, 28618828, 887468400, 27512793028, 852892846848, 26439623851900, 819628237654128], "abvar_counts_str": "28 1008 30100 923328 28618828 887468400 27512793028 852892846848 26439623851900 819628237654128 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.383045975359039], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 28, "curve_counts": [28, 1008, 30100, 923328, 28618828, 887468400, 27512793028, 852892846848, 26439623851900, 819628237654128], "curve_counts_str": "28 1008 30100 923328 28618828 887468400 27512793028 852892846848 26439623851900 819628237654128 ", "curves": ["y^2=x^3+15*x+15", "y^2=x^3+15", "y^2=x^3+5*x+5", "y^2=x^3+7*x+21", "y^2=x^3+16*x+17", "y^2=x^3+10*x+10"], "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": 4, "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_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 6, "label": "1.31.ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["2.0.3.1"], "p": 31, "p_rank": 1, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 3]], "poly": [1, -4, 31], "poly_str": "1 -4 31 ", "primitive_models": [], "principal_polarization_count": 6, "q": 31, "real_poly": [1, -4], "simple_distinct": ["1.31.ae"], "simple_factors": ["1.31.aeA"], "simple_multiplicities": [1], "singular_primes": ["3,-F-1", "2,F+1"], "size": 6, "slopes": ["0A", "1A"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 6, "twists": [["1.31.e", "1.961.bu", 2], ["1.31.ah", "1.29791.lw", 3], ["1.31.l", "1.29791.lw", 3], ["1.31.al", "1.887503681.acafa", 6], ["1.31.h", "1.887503681.acafa", 6]], "weak_equivalence_count": 4, "zfv_index": 6, "zfv_index_factorization": [[2, 1], [3, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 3, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 108, "zfv_singular_count": 4, "zfv_singular_primes": ["3,-F-1", "2,F+1"]}