# Stored data for abelian variety isogeny class 2.19.a_h, downloaded from the LMFDB on 12 September 2026.
{"abvar_count": 369, "abvar_counts": [369, 136161, 47038644, 17159690025, 6131070216729, 2212634029358736, 799006684061789649, 288434882201789270025, 104127350298553606787604, 37590022002461387031459441], "abvar_counts_str": "369 136161 47038644 17159690025 6131070216729 2212634029358736 799006684061789649 288434882201789270025 104127350298553606787604 37590022002461387031459441 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.279486410696411, 0.720513589303589], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 376, 6860, 131668, 2476100, 47031406, 893871740, 16983178468, 322687697780, 6131074175656], "curve_counts_str": "20 376 6860 131668 2476100 47031406 893871740 16983178468 322687697780 6131074175656 ", "curves": ["y^2=18*x^6+5*x^5+10*x^4+11*x^3+12*x^2+2*x+6", "y^2=8*x^6+2*x^5+2*x^4+13*x^3+14*x^2+4*x+12", "y^2=16*x^6+4*x^5+4*x^4+7*x^3+9*x^2+8*x+5", "y^2=13*x^6+18*x^5+5*x^4+5*x^3+11*x^2+11*x+8", "y^2=14*x^6+x^5+x^4+11*x^3+4*x^2+7*x+17", "y^2=9*x^6+2*x^5+2*x^4+3*x^3+8*x^2+14*x+15", "y^2=3*x^6+16*x^5+3*x^4+18*x^2+10*x+18", "y^2=6*x^6+13*x^5+6*x^4+17*x^2+x+17", "y^2=3*x^6+17*x^5+15*x^4+15*x^3+8*x^2+7*x+18", "y^2=3*x^6+9*x^5+2*x^4+11*x^3+10*x+14", "y^2=6*x^6+18*x^5+4*x^4+3*x^3+x+9", "y^2=7*x^6+5*x^5+13*x^4+5*x^3+17*x^2+3*x+12", "y^2=7*x^6+4*x^5+6*x^4+11*x^3+12*x^2+16*x+4", "y^2=14*x^6+8*x^5+12*x^4+3*x^3+5*x^2+13*x+8", "y^2=5*x^6+3*x^5+x^4+3*x^3+10*x^2+16*x+13", "y^2=13*x^6+11*x^5+13*x^4+5*x^3+x^2+x+4", "y^2=7*x^6+3*x^5+7*x^4+10*x^3+2*x^2+2*x+8", "y^2=15*x^6+12*x^5+5*x^4+6*x^3+2*x^2+5*x+3", "y^2=2*x^6+16*x^5+5*x^4+3*x^3+18*x^2+14*x+3", "y^2=4*x^6+13*x^5+10*x^4+6*x^3+17*x^2+9*x+6", "y^2=13*x^6+3*x^5+11*x^4+8*x^3+11*x^2+11*x+3", "y^2=7*x^6+6*x^5+3*x^4+16*x^3+3*x^2+3*x+6", "y^2=13*x^6+14*x^5+7*x^4+2*x^3+8*x^2+x+4", "y^2=7*x^6+9*x^5+14*x^4+4*x^3+16*x^2+2*x+8", "y^2=14*x^6+18*x^5+2*x^4+15*x^3+10*x^2+14*x+5", "y^2=9*x^6+17*x^5+4*x^4+11*x^3+x^2+9*x+10", "y^2=2*x^6+8*x^5+4*x^4+6*x^3+13*x^2+7*x+4", "y^2=4*x^6+16*x^5+8*x^4+12*x^3+7*x^2+14*x+8", "y^2=16*x^6+3*x^5+4*x^4+2*x^3+8*x^2+8*x+7", "y^2=13*x^6+6*x^5+8*x^4+4*x^3+16*x^2+16*x+14"], "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": ["2.0.155.1"], "geometric_splitting_field": "2.0.155.1", "geometric_splitting_polynomials": [[39, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 30, "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": 30, "label": "2.19.a_h", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["4.0.384400.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 2], [1, 5, 2, 2], [1, 23, 1, 4]], "poly": [1, 0, 7, 0, 361], "poly_str": "1 0 7 0 361 ", "primitive_models": [], "principal_polarization_count": 36, "q": 19, "real_poly": [1, 0, -31], "simple_distinct": ["2.19.a_h"], "simple_factors": ["2.19.a_hA"], "simple_multiplicities": [1], "singular_primes": ["3,5*V+5", "3,2*F-3*V-2"], "size": 36, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.384400.1", "splitting_polynomials": [[81, 0, -13, 0, 1]], "twist_count": 2, "twists": [["2.19.a_ah", "2.130321.bzu_boppb", 4]], "weak_equivalence_count": 4, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 16, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2025, "zfv_singular_count": 4, "zfv_singular_primes": ["3,5*V+5", "3,2*F-3*V-2"]}