# Stored data for abelian variety isogeny class 1.71.ae, downloaded from the LMFDB on 12 October 2026.
{"abvar_count": 68, "abvar_counts": [68, 5168, 358700, 25405888, 1804150228, 128100378800, 9095126155708, 645753548498688, 45848500361651300, 3255243548357732528], "abvar_counts_str": "68 5168 358700 25405888 1804150228 128100378800 9095126155708 645753548498688 45848500361651300 3255243548357732528 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.423719104037511], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 68, "curve_counts": [68, 5168, 358700, 25405888, 1804150228, 128100378800, 9095126155708, 645753548498688, 45848500361651300, 3255243548357732528], "curve_counts_str": "68 5168 358700 25405888 1804150228 128100378800 9095126155708 645753548498688 45848500361651300 3255243548357732528 ", "curves": ["y^2=x^3+44*x+44", "y^2=x^3+60*x+65", "y^2=x^3+54*x+54", "y^2=x^3+43*x+43"], "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": ["2.0.67.1"], "geometric_splitting_field": "2.0.67.1", "geometric_splitting_polynomials": [[17, -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": 4, "label": "1.71.ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["2.0.67.1"], "p": 71, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -4, 71], "poly_str": "1 -4 71 ", "primitive_models": [], "principal_polarization_count": 4, "q": 71, "real_poly": [1, -4], "simple_distinct": ["1.71.ae"], "simple_factors": ["1.71.aeA"], "simple_multiplicities": [1], "singular_primes": ["2,F-1"], "size": 4, "slopes": ["0A", "1A"], "splitting_field": "2.0.67.1", "splitting_polynomials": [[17, -1, 1]], "twist_count": 2, "twists": [["1.71.e", "1.5041.ew", 2]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 268, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F-1"]}