# Stored data for abelian variety isogeny class 2.13.a_ac, downloaded from the LMFDB on 09 December 2025.
{"abvar_count": 168, "abvar_counts": [168, 28224, 4827816, 834978816, 137858212968, 23307807329856, 3937376450113512, 665327806805458944, 112455406938408191784, 19004886882730443369024], "abvar_counts_str": "168 28224 4827816 834978816 137858212968 23307807329856 3937376450113512 665327806805458944 112455406938408191784 19004886882730443369024 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.237745206150638, 0.762254793849362], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 14, "curve_counts": [14, 166, 2198, 29230, 371294, 4828822, 62748518, 815621854, 10604499374, 137857934086], "curve_counts_str": "14 166 2198 29230 371294 4828822 62748518 815621854 10604499374 137857934086 ", "curves": ["y^2=4*x^6+5*x^5+9*x^4+12*x^3+7*x^2+6*x+5", "y^2=8*x^6+10*x^5+5*x^4+11*x^3+x^2+12*x+10", "y^2=2*x^5+9*x^4+4*x^3+4*x+2", "y^2=x^6+x^5+11*x^4+7*x^3+8*x^2+5*x+12", "y^2=3*x^5+4*x^4+5*x^3+7*x^2+10*x", "y^2=12*x^6+2*x^5+12*x^4+4*x^3+6*x^2+12*x+1", "y^2=11*x^6+4*x^5+11*x^4+8*x^3+12*x^2+11*x+2", "y^2=8*x^5+11*x^3+10*x^2+5*x+9", "y^2=3*x^5+9*x^3+7*x^2+10*x+5", "y^2=4*x^6+5*x^5+3*x^4+7*x^3+4*x^2+8*x+12", "y^2=6*x^6+5*x^5+6*x^4+12*x^3+6*x^2+7*x", "y^2=12*x^6+10*x^5+12*x^4+11*x^3+12*x^2+x", "y^2=10*x^6+x^5+11*x^4+5*x^3+3*x^2+6", "y^2=5*x^6+8*x^4+9*x^3+x^2+5*x+2", "y^2=12*x^5+12*x^4+11*x^3+x^2+8*x+6", "y^2=11*x^5+11*x^4+9*x^3+2*x^2+3*x+12", "y^2=x^6+9*x^5+5*x^4+7*x^3+x^2+5*x+3", "y^2=3*x^6+2*x^5+11*x^4+6*x^3+12*x^2+7*x+2", "y^2=2*x^6+8*x^3+6*x^2+11*x+11", "y^2=4*x^6+3*x^3+12*x^2+9*x+9", "y^2=8*x^5+7*x^4+4*x^2+8*x+1", "y^2=3*x^5+x^4+8*x^2+3*x+2"], "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": 4, "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": ["2.0.168.1"], "geometric_splitting_field": "2.0.168.1", "geometric_splitting_polynomials": [[42, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 22, "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": 22, "label": "2.13.a_ac", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.112896.6"], "p": 13, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -2, 0, 169], "poly_str": "1 0 -2 0 169 ", "primitive_models": [], "q": 13, "real_poly": [1, 0, -28], "simple_distinct": ["2.13.a_ac"], "simple_factors": ["2.13.a_acA"], "simple_multiplicities": [1], "singular_primes": ["2,9*V-1"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.112896.6", "splitting_polynomials": [[81, 0, 24, 0, 1]], "twist_count": 2, "twists": [["2.13.a_c", "2.28561.zs_jpnq", 4]], "weak_equivalence_count": 5, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 576, "zfv_singular_count": 2, "zfv_singular_primes": ["2,9*V-1"]}