# Stored data for abelian variety isogeny class 2.7.ae_j, downloaded from the LMFDB on 27 October 2025.
{"abvar_count": 27, "abvar_counts": [27, 2457, 104976, 5545449, 286480827, 13908900096, 677804147019, 33256196289225, 1629429133651344, 79798504121221977], "abvar_counts_str": "27 2457 104976 5545449 286480827 13908900096 677804147019 33256196289225 1629429133651344 79798504121221977 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.106147807504828, 0.560518859161838], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 4, "curve_counts": [4, 52, 304, 2308, 17044, 118222, 823036, 5768836, 40378768, 282497332], "curve_counts_str": "4 52 304 2308 17044 118222 823036 5768836 40378768 282497332 ", "curves": ["y^2=6*x^6+4*x^5+3*x^3+x+5", "y^2=3*x^6+5*x^4+3*x^3+5*x^2+3", "y^2=3*x^6+2*x^5+2*x^3+5*x^2+2*x+3", "y^2=x^6+4", "y^2=3*x^6+4*x^5+x^4+x^2+x+6", "y^2=3*x^6+2*x^5+6*x^4+3*x^3+2*x^2+6*x+5"], "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": 10, "g": 2, "galois_groups": ["2T1", "2T1"], "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 6, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 6, "label": "2.7.ae_j", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.3.1", "2.0.3.1"], "p": 7, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 3]], "poly": [1, -4, 9, -28, 49], "poly_str": "1 -4 9 -28 49 ", "primitive_models": [], "principal_polarization_count": 8, "q": 7, "real_poly": [1, -4, -5], "simple_distinct": ["1.7.af", "1.7.b"], "simple_factors": ["1.7.afA", "1.7.bA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,5*F-2", "2,F^2-4*F-V"], "size": 14, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.7.ag_t", "2.49.c_abt", 2], ["2.7.e_j", "2.49.c_abt", 2], ["2.7.g_t", "2.49.c_abt", 2], ["2.7.ak_bn", "2.343.abo_bpu", 3], ["2.7.ab_ag", "2.343.abo_bpu", 3], ["2.7.c_p", "2.343.abo_bpu", 3], ["2.7.f_s", "2.343.abo_bpu", 3], ["2.7.i_be", "2.343.abo_bpu", 3], ["2.7.aj_bi", "2.117649.wa_sbby", 6], ["2.7.ai_be", "2.117649.wa_sbby", 6], ["2.7.ag_t", "2.117649.wa_sbby", 6], ["2.7.af_s", "2.117649.wa_sbby", 6], ["2.7.ad_k", "2.117649.wa_sbby", 6], ["2.7.ac_p", "2.117649.wa_sbby", 6], ["2.7.a_al", "2.117649.wa_sbby", 6], ["2.7.a_ac", "2.117649.wa_sbby", 6], ["2.7.a_n", "2.117649.wa_sbby", 6], ["2.7.b_ag", "2.117649.wa_sbby", 6], ["2.7.d_k", "2.117649.wa_sbby", 6], ["2.7.e_j", "2.117649.wa_sbby", 6], ["2.7.g_t", "2.117649.wa_sbby", 6], ["2.7.j_bi", "2.117649.wa_sbby", 6], ["2.7.k_bn", "2.117649.wa_sbby", 6], ["2.7.a_an", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.a_c", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.a_l", "2.13841287201.rmdw_gjxcinog", 12]], "weak_equivalence_count": 12, "zfv_index": 108, "zfv_index_factorization": [[2, 2], [3, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 3, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 81, "zfv_singular_count": 4, "zfv_singular_primes": ["3,5*F-2", "2,F^2-4*F-V"]}