# Stored data for abelian variety isogeny class 2.5.ae_l, downloaded from the LMFDB on 25 April 2026.
{"abvar_count": 13, "abvar_counts": [13, 793, 16900, 381433, 10005853, 251539600, 6147184693, 152176891113, 3809093856100, 95362793192953], "abvar_counts_str": "13 793 16900 381433 10005853 251539600 6147184693 152176891113 3809093856100 95362793192953 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.1857497156829, 0.480916950983767], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 2, "curve_counts": [2, 32, 134, 612, 3202, 16094, 78682, 389572, 1950254, 9765152], "curve_counts_str": "2 32 134 612 3202 16094 78682 389572 1950254 9765152 ", "curves": ["y^2=x^6+4*x^5+3*x^4+2*x^3+4*x^2+2*x+2", "y^2=3*x^6+4*x^5+3*x^4+4*x^3+3"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "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": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.4.1"], "geometric_splitting_field": "2.0.4.1", "geometric_splitting_polynomials": [[1, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 2, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 2, "label": "2.5.ae_l", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.144.1"], "p": 5, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [], "poly": [1, -4, 11, -20, 25], "poly_str": "1 -4 11 -20 25 ", "primitive_models": [], "principal_polarization_count": 2, "q": 5, "real_poly": [1, -4, 1], "simple_distinct": ["2.5.ae_l"], "simple_factors": ["2.5.ae_lA"], "simple_multiplicities": [1], "singular_primes": ["11,15*F+5*V-25"], "size": 2, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.144.1", "splitting_polynomials": [[1, 0, -1, 0, 1]], "twist_count": 16, "twists": [["2.5.e_l", "2.25.g_l", 2], ["2.5.i_ba", "2.125.i_kg", 3], ["2.5.ac_ab", "2.625.ao_aqn", 4], ["2.5.c_ab", "2.625.ao_aqn", 4], ["2.5.ai_ba", "2.15625.sa_exfy", 6], ["2.5.a_ag", "2.15625.sa_exfy", 6], ["2.5.ag_s", "2.244140625.acroe_djppwqg", 12], ["2.5.ae_o", "2.244140625.acroe_djppwqg", 12], ["2.5.ac_c", "2.244140625.acroe_djppwqg", 12], ["2.5.a_g", "2.244140625.acroe_djppwqg", 12], ["2.5.c_c", "2.244140625.acroe_djppwqg", 12], ["2.5.e_o", "2.244140625.acroe_djppwqg", 12], ["2.5.g_s", "2.244140625.acroe_djppwqg", 12], ["2.5.a_ai", "2.59604644775390625.akvffce_bhpsebnknczgg", 24], ["2.5.a_i", "2.59604644775390625.akvffce_bhpsebnknczgg", 24]], "weak_equivalence_count": 2, "zfv_index": 11, "zfv_index_factorization": [[11, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 1, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 121, "zfv_singular_count": 2, "zfv_singular_primes": ["11,15*F+5*V-25"]}