# Stored data for abelian variety isogeny class 1.61.an, downloaded from the LMFDB on 03 December 2025.
{"abvar_count": 49, "abvar_counts": [49, 3675, 227164, 13851075, 844653229, 51520795200, 3142744834369, 191707313304675, 11694145974931084, 713342910111391875], "abvar_counts_str": "49 3675 227164 13851075 844653229 51520795200 3142744834369 191707313304675 11694145974931084 713342910111391875 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.187058313935084], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 49, "curve_counts": [49, 3675, 227164, 13851075, 844653229, 51520795200, 3142744834369, 191707313304675, 11694145974931084, 713342910111391875], "curve_counts_str": "49 3675 227164 13851075 844653229 51520795200 3142744834369 191707313304675 11694145974931084 713342910111391875 ", "curves": ["y^2=x^3+31*x+1", "y^2=x^3+10", "y^2=x^3+25*x+50"], "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 3, "label": "1.61.an", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.3.1"], "p": 61, "p_rank": 1, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2]], "poly": [1, -13, 61], "poly_str": "1 -13 61 ", "primitive_models": [], "principal_polarization_count": 3, "q": 61, "real_poly": [1, -13], "simple_distinct": ["1.61.an"], "simple_factors": ["1.61.anA"], "simple_multiplicities": [1], "singular_primes": ["5,F-9"], "size": 3, "slopes": ["0A", "1A"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 6, "twists": [["1.61.n", "1.3721.abv", 2], ["1.61.ab", "1.226981.ha", 3], ["1.61.o", "1.226981.ha", 3], ["1.61.ao", "1.51520374361.xyoc", 6], ["1.61.b", "1.51520374361.xyoc", 6]], "weak_equivalence_count": 2, "zfv_index": 5, "zfv_index_factorization": [[5, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 2, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 75, "zfv_singular_count": 2, "zfv_singular_primes": ["5,F-9"]}