# Stored data for abelian variety isogeny class 2.7.a_c, downloaded from the LMFDB on 27 July 2026.
{"abvar_count": 52, "abvar_counts": [52, 2704, 117364, 6230016, 282497332, 13774308496, 678221683828, 33186447949824, 1628413675459636, 79804742587118224], "abvar_counts_str": "52 2704 117364 6230016 282497332 13774308496 678221683828 33186447949824 1628413675459636 79804742587118224 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.272814474171495, 0.727185525828505], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 8, "curve_counts": [8, 54, 344, 2590, 16808, 117078, 823544, 5756734, 40353608, 282519414], "curve_counts_str": "8 54 344 2590 16808 117078 823544 5756734 40353608 282519414 ", "curves": ["y^2=5*x^6+5*x^4+5*x^3+x^2+5*x", "y^2=x^6+x^4+x^3+3*x^2+x", "y^2=x^6+4*x^5+3*x^4+4*x^3+3*x^2+x", "y^2=5*x^6+6*x^5+x^4+6*x^3+3*x^2+5*x+2", "y^2=6*x^6+3*x^5+3*x^3+5*x+1", "y^2=x^6+6*x^5+2*x^4+4*x^3+5*x^2+6*x+6", "y^2=x^6+4*x^5+5*x^4+5*x^3+3*x^2+x+6", "y^2=5*x^6+4*x^5+3*x^4+x^3+x^2+2*x+2", "y^2=5*x^6+x^5+x^4+4*x^3+5*x", "y^2=x^6+3*x^5+3*x^4+5*x^3+x"], "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": 7, "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": 2, "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": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 10, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 10, "label": "2.7.a_c", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.144.1"], "p": 7, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 2, 0, 49], "poly_str": "1 0 2 0 49 ", "primitive_models": [], "q": 7, "real_poly": [1, 0, -12], "simple_distinct": ["2.7.a_c"], "simple_factors": ["2.7.a_cA"], "simple_multiplicities": [1], "singular_primes": ["2,V+1"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.144.1", "splitting_polynomials": [[1, 0, -1, 0, 1]], "twist_count": 24, "twists": [["2.7.a_an", "2.343.a_ala", 3], ["2.7.a_l", "2.343.a_ala", 3], ["2.7.ai_be", "2.2401.hg_ueo", 4], ["2.7.a_ac", "2.2401.hg_ueo", 4], ["2.7.i_be", "2.2401.hg_ueo", 4], ["2.7.ak_bn", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.aj_bi", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.ag_t", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.af_s", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.ae_j", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.ad_k", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.ac_p", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.ab_ag", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.a_al", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.a_n", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.b_ag", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.c_p", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.d_k", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.e_j", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.f_s", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.g_t", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.j_bi", "2.13841287201.rmdw_gjxcinog", 12], ["2.7.k_bn", "2.13841287201.rmdw_gjxcinog", 12]], "weak_equivalence_count": 7, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 256, "zfv_singular_count": 2, "zfv_singular_primes": ["2,V+1"]}