# Stored data for abelian variety isogeny class 1.61.ae, downloaded from the LMFDB on 28 October 2025.
{"abvar_count": 58, "abvar_counts": [58, 3828, 227650, 13842048, 844540378, 51520382100, 3142746278338, 191707326294528, 11694145936041850, 713342910224581428], "abvar_counts_str": "58 3828 227650 13842048 844540378 51520382100 3142746278338 191707326294528 11694145936041850 713342910224581428 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.417571001239811], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 58, "curve_counts": [58, 3828, 227650, 13842048, 844540378, 51520382100, 3142746278338, 191707326294528, 11694145936041850, 713342910224581428], "curve_counts_str": "58 3828 227650 13842048 844540378 51520382100 3142746278338 191707326294528 11694145936041850 713342910224581428 ", "curves": ["y^2=x^3+57*x+57", "y^2=x^3+8*x+8", "y^2=x^3+52*x+43", "y^2=x^3+56*x+56"], "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": ["2.0.228.1"], "geometric_splitting_field": "2.0.228.1", "geometric_splitting_polynomials": [[57, 0, 1]], "group_structure_count": 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": 4, "label": "1.61.ae", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "number_fields": ["2.0.228.1"], "p": 61, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -4, 61], "poly_str": "1 -4 61 ", "primitive_models": [], "principal_polarization_count": 4, "q": 61, "real_poly": [1, -4], "simple_distinct": ["1.61.ae"], "simple_factors": ["1.61.aeA"], "simple_multiplicities": [1], "singular_primes": [], "size": 4, "slopes": ["0A", "1A"], "splitting_field": "2.0.228.1", "splitting_polynomials": [[57, 0, 1]], "twist_count": 2, "twists": [["1.61.e", "1.3721.ec", 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": 228, "zfv_singular_count": 0, "zfv_singular_primes": []}