# Stored data for abelian variety isogeny class 2.13.a_i, downloaded from the LMFDB on 14 March 2026.
{"abvar_count": 178, "abvar_counts": [178, 31684, 4823266, 831514896, 137859234418, 23263894906756, 3937376283455842, 665387319878221824, 112455406958763613234, 19005168514317075798724], "abvar_counts_str": "178 31684 4823266 831514896 137859234418 23263894906756 3937376283455842 665387319878221824 112455406958763613234 19005168514317075798724 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.299778369831645, 0.700221630168355], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 14, "curve_counts": [14, 186, 2198, 29110, 371294, 4819722, 62748518, 815694814, 10604499374, 137859976986], "curve_counts_str": "14 186 2198 29110 371294 4819722 62748518 815694814 10604499374 137859976986 ", "curves": ["y^2=x^6+x^5+6*x^4+12*x^2+9*x+8", "y^2=2*x^6+5*x^4+6*x^3+3*x^2+3*x+12", "y^2=4*x^6+10*x^4+12*x^3+6*x^2+6*x+11", "y^2=9*x^6+6*x^5+4*x^4+8*x^2+2*x+7", "y^2=12*x^6+7*x^5+11*x^4+2*x^3+4*x^2+5*x+2", "y^2=11*x^6+x^5+9*x^4+4*x^3+8*x^2+10*x+4", "y^2=3*x^5+4*x^4+10*x^3+6*x^2+11*x+1", "y^2=6*x^5+8*x^4+7*x^3+12*x^2+9*x+2", "y^2=12*x^6+8*x^5+3*x^4+4*x^3+5*x^2+9*x+3", "y^2=11*x^6+3*x^5+6*x^4+8*x^3+10*x^2+5*x+6", "y^2=4*x^6+2*x^5+10*x^3+11", "y^2=8*x^6+4*x^5+7*x^3+9", "y^2=10*x^6+6*x^5+9*x^4+3*x^3+x^2+12*x+7", "y^2=7*x^6+12*x^5+5*x^4+6*x^3+2*x^2+11*x+1", "y^2=12*x^6+7*x^5+7*x^4+5*x^3+12*x^2+9*x+7", "y^2=11*x^6+x^5+x^4+10*x^3+11*x^2+5*x+1", "y^2=11*x^5+9*x^4+12*x^3+5*x^2+9*x+6", "y^2=9*x^5+5*x^4+11*x^3+10*x^2+5*x+12"], "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.68.1"], "geometric_splitting_field": "2.0.68.1", "geometric_splitting_polynomials": [[17, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 18, "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": 18, "label": "2.13.a_i", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.73984.1"], "p": 13, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 7, 1, 4], [1, 7, 3, 4]], "poly": [1, 0, 8, 0, 169], "poly_str": "1 0 8 0 169 ", "primitive_models": [], "principal_polarization_count": 24, "q": 13, "real_poly": [1, 0, -18], "simple_distinct": ["2.13.a_i"], "simple_factors": ["2.13.a_iA"], "simple_multiplicities": [1], "singular_primes": ["3,8*F^2-10"], "size": 24, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.73984.1", "splitting_polynomials": [[81, 0, 16, 0, 1]], "twist_count": 4, "twists": [["2.13.a_ai", "2.28561.vc_hnoo", 4], ["2.13.ag_s", "2.815730721.acbdc_gilnjwo", 8], ["2.13.g_s", "2.815730721.acbdc_gilnjwo", 8]], "weak_equivalence_count": 2, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 16, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 1156, "zfv_singular_count": 2, "zfv_singular_primes": ["3,8*F^2-10"]}