# Stored data for abelian variety isogeny class 1.337.ar, downloaded from the LMFDB on 29 October 2025.
{"abvar_count": 321, "abvar_counts": [321, 113955, 38285028, 12897996675, 4346595490641, 1464803548093440, 493638820363124673, 166356282589087827075, 56062067226367800297636, 18892916655138614252206275], "abvar_counts_str": "321 113955 38285028 12897996675 4346595490641 1464803548093440 493638820363124673 166356282589087827075 56062067226367800297636 18892916655138614252206275 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.34676418837729], "center_dim": 2, "curve_count": 321, "curve_counts": [321, 113955, 38285028, 12897996675, 4346595490641, 1464803548093440, 493638820363124673, 166356282589087827075, 56062067226367800297636, 18892916655138614252206275], "curve_counts_str": "321 113955 38285028 12897996675 4346595490641 1464803548093440 493638820363124673 166356282589087827075 56062067226367800297636 18892916655138614252206275 ", "curves": ["y^2=x^3+143*x+143", "y^2=x^3+16*x+16", "y^2=x^3+293*x+117", "y^2=x^3+272*x+272", "y^2=x^3+201*x+331", "y^2=x^3+139*x+21"], "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": ["2.0.1059.1"], "geometric_splitting_field": "2.0.1059.1", "geometric_splitting_polynomials": [[265, -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": 6, "label": "1.337.ar", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.1059.1"], "p": 337, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -17, 337], "poly_str": "1 -17 337 ", "primitive_models": [], "principal_polarization_count": 6, "q": 337, "real_poly": [1, -17], "simple_distinct": ["1.337.ar"], "simple_factors": ["1.337.arA"], "simple_multiplicities": [1], "size": 6, "slopes": ["0A", "1A"], "splitting_field": "2.0.1059.1", "splitting_polynomials": [[265, -1, 1]], "twist_count": 2, "twists": [["1.337.r", "1.113569.ov", 2]]}