# Stored data for abelian variety isogeny class 1.61.ap, downloaded from the LMFDB on 12 December 2025.
{"abvar_count": 47, "abvar_counts": [47, 3619, 226352, 13842675, 844587227, 51520431424, 3142744245527, 191707330659075, 11694146271781232, 713342913269719579], "abvar_counts_str": "47 3619 226352 13842675 844587227 51520431424 3142744245527 191707330659075 11694146271781232 713342913269719579 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 1, "angles": [0.0900194921158871], "center_dim": 2, "cohen_macaulay_max": 1, "curve_count": 47, "curve_counts": [47, 3619, 226352, 13842675, 844587227, 51520431424, 3142744245527, 191707330659075, 11694146271781232, 713342913269719579], "curve_counts_str": "47 3619 226352 13842675 844587227 51520431424 3142744245527 191707330659075 11694146271781232 713342913269719579 ", "curves": ["y^2=x^3+18*x+36"], "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": ["2.0.19.1"], "geometric_splitting_field": "2.0.19.1", "geometric_splitting_polynomials": [[5, -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": 1, "label": "1.61.ap", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.19.1"], "p": 61, "p_rank": 1, "p_rank_deficit": 0, "poly": [1, -15, 61], "poly_str": "1 -15 61 ", "primitive_models": [], "principal_polarization_count": 1, "q": 61, "real_poly": [1, -15], "simple_distinct": ["1.61.ap"], "simple_factors": ["1.61.apA"], "simple_multiplicities": [1], "singular_primes": [], "size": 1, "slopes": ["0A", "1A"], "splitting_field": "2.0.19.1", "splitting_polynomials": [[5, -1, 1]], "twist_count": 2, "twists": [["1.61.p", "1.3721.adz", 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": 19, "zfv_singular_count": 0, "zfv_singular_primes": []}