# Stored data for abelian variety isogeny class 1.431.abb, downloaded from the LMFDB on 02 November 2025.
{"abvar_count": 405, "abvar_counts": [405, 185895, 80078220, 34507502955, 14872584261375, 6410082456100080, 2762745566283812745, 1190743340402747578995, 513210379737672945759780, 221193673667012298713817375], "abvar_counts_str": "405 185895 80078220 34507502955 14872584261375 6410082456100080 2762745566283812745 1190743340402747578995 513210379737672945759780 221193673667012298713817375 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.274654880019371], "center_dim": 2, "curve_count": 405, "curve_counts": [405, 185895, 80078220, 34507502955, 14872584261375, 6410082456100080, 2762745566283812745, 1190743340402747578995, 513210379737672945759780, 221193673667012298713817375], "curve_counts_str": "405 185895 80078220 34507502955 14872584261375 6410082456100080 2762745566283812745 1190743340402747578995 513210379737672945759780 221193673667012298713817375 ", "curves": ["y^2=x^3+178*x+384", "y^2=x^3+403*x+235", "y^2=x^3+294*x+334", "y^2=x^3+142*x+132", "y^2=x^3+378*x+60", "y^2=x^3+262*x+262", "y^2=x^3+98*x+98", "y^2=x^3+25*x+25"], "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, "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": ["2.0.995.1"], "geometric_splitting_field": "2.0.995.1", "geometric_splitting_polynomials": [[249, -1, 1]], "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": 8, "label": "1.431.abb", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.995.1"], "p": 431, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -27, 431], "poly_str": "1 -27 431 ", "primitive_models": [], "principal_polarization_count": 8, "q": 431, "real_poly": [1, -27], "simple_distinct": ["1.431.abb"], "simple_factors": ["1.431.abbA"], "simple_multiplicities": [1], "size": 8, "slopes": ["0A", "1A"], "splitting_field": "2.0.995.1", "splitting_polynomials": [[249, -1, 1]], "twist_count": 2, "twists": [["1.431.bb", "1.185761.fd", 2]]}