# Stored data for abelian variety isogeny class 2.19.c_x, downloaded from the LMFDB on 13 June 2026.
{"abvar_count": 425, "abvar_counts": [425, 146625, 46926800, 17040317625, 6124092709625, 2212425929376000, 799088834639269025, 288444832619465723625, 104127098349146792411600, 37589975064623067246290625], "abvar_counts_str": "425 146625 46926800 17040317625 6124092709625 2212425929376000 799088834639269025 288444832619465723625 104127098349146792411600 37589975064623067246290625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.388176076176801, 0.69443002753289], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 22, "curve_counts": [22, 404, 6844, 130756, 2473282, 47026982, 893963638, 16983764356, 322686916996, 6131066519924], "curve_counts_str": "22 404 6844 130756 2473282 47026982 893963638 16983764356 322686916996 6131066519924 ", "curves": ["y^2=8*x^6+17*x^5+13*x^4+18*x^3+13*x^2+17*x+8", "y^2=17*x^6+2*x^4+18*x^3+10*x^2+4*x+14", "y^2=3*x^6+10*x^5+x^4+3*x^3+x^2+10*x+3", "y^2=3*x^6+10*x^5+6*x^4+10*x^3+16*x^2+11*x+2", "y^2=16*x^6+9*x^5+6*x^4+4*x^3+6*x^2+9*x+16", "y^2=9*x^6+14*x^5+13*x^3+7*x+5", "y^2=16*x^6+16*x^5+14*x^4+7*x^3+14*x^2+16*x+16", "y^2=3*x^6+x^5+7*x^4+12*x^3+18*x^2+15*x+7", "y^2=14*x^6+4*x^5+10*x^4+18*x^3+2*x^2+7*x+6", "y^2=11*x^6+12*x^5+6*x^4+6*x^3+8*x^2+8*x+3", "y^2=16*x^6+10*x^5+2*x^4+4*x^3+4*x^2+18*x+8", "y^2=15*x^6+6*x^5+8*x^4+17*x^3+9*x^2+18*x+6", "y^2=9*x^6+7*x^4+17*x^3+15*x^2+x+16", "y^2=12*x^6+12*x^5+15*x^4+12*x^3+8*x^2+5*x+7", "y^2=7*x^6+5*x^5+5*x^4+16*x^3+3*x^2+17*x+13", "y^2=x^6+3*x^5+3*x^4+8*x^3+9*x^2+17*x+13", "y^2=11*x^6+2*x^5+17*x^4+5*x^3+17*x^2+2*x+11", "y^2=17*x^6+11*x^5+7*x^4+11*x^3+7*x^2+11*x+17", "y^2=16*x^6+11*x^5+9*x^4+3*x^3+6*x^2+12*x+3", "y^2=10*x^6+15*x^5+5*x^4+2*x^3+18*x^2+3*x+18", "y^2=6*x^6+8*x^5+6*x^4+17*x^3+14*x^2+10*x+16", "y^2=12*x^6+3*x^5+15*x^4+3*x^3+18*x^2+9*x+7", "y^2=17*x^6+7*x^5+6*x^4+18*x^3+16*x^2+9*x+7", "y^2=3*x^6+16*x^5+5*x^4+2*x^3+15*x^2+x+6"], "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": 4, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.67.1", "2.0.51.1"], "geometric_splitting_field": "4.0.11675889.1", "geometric_splitting_polynomials": [[16, 0, 59, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 24, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 24, "label": "2.19.c_x", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.67.1", "2.0.51.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[2, 3, 1, 4], [2, 5, 1, 6], [2, 13, 1, 6]], "poly": [1, 2, 23, 38, 361], "poly_str": "1 2 23 38 361 ", "primitive_models": [], "principal_polarization_count": 26, "q": 19, "real_poly": [1, 2, -15], "simple_distinct": ["1.19.ad", "1.19.f"], "simple_factors": ["1.19.adA", "1.19.fA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F^2-3*V"], "size": 68, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.11675889.1", "splitting_polynomials": [[16, 0, 59, 0, 1]], "twist_count": 4, "twists": [["2.19.ai_cb", "2.361.bq_bqh", 2], ["2.19.ac_x", "2.361.bq_bqh", 2], ["2.19.i_cb", "2.361.bq_bqh", 2]], "weak_equivalence_count": 4, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 48, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3417, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2-3*V"]}