# Stored data for abelian variety isogeny class 2.5.ae_n, downloaded from the LMFDB on 03 September 2025.
{"abvar_count": 15, "abvar_counts": [15, 945, 20160, 401625, 9628575, 243855360, 6107451015, 152251619625, 3808015968960, 95358161970225], "abvar_counts_str": "15 945 20160 401625 9628575 243855360 6107451015 152251619625 3808015968960 95358161970225 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.26594214021463, 0.428216853435647], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 2, "curve_counts": [2, 36, 158, 644, 3082, 15606, 78178, 389764, 1949702, 9764676], "curve_counts_str": "2 36 158 644 3082 15606 78178 389764 1949702 9764676 ", "curves": ["y^2=3*x^6+x^4+x^3+x^2+3", "y^2=2*x^6+2*x^5+x^4+3*x^3+x^2+2*x+2", "y^2=3*x^6+2*x^5+x^4+x^2+2*x+3"], "dim1_distinct": 2, "dim1_factors": 2, "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": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "geom_dim1_factors": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.11.1", "2.0.19.1"], "geometric_splitting_field": "4.0.43681.2", "geometric_splitting_polynomials": [[4, 0, 15, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 3, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 3, "label": "2.5.ae_n", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.11.1", "2.0.19.1"], "p": 5, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -4, 13, -20, 25], "poly_str": "1 -4 13 -20 25 ", "primitive_models": [], "q": 5, "real_poly": [1, -4, 3], "simple_distinct": ["1.5.ad", "1.5.ab"], "simple_factors": ["1.5.adA", "1.5.abA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,-F^2-F+7"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.43681.2", "splitting_polynomials": [[4, 0, 15, 0, 1]], "twist_count": 4, "twists": [["2.5.ac_h", "2.25.k_ch", 2], ["2.5.c_h", "2.25.k_ch", 2], ["2.5.e_n", "2.25.k_ch", 2]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 209, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F^2-F+7"]}