# Stored data for abelian variety isogeny class 2.19.a_ah, downloaded from the LMFDB on 10 December 2025.
{"abvar_count": 355, "abvar_counts": [355, 126025, 47053120, 17159690025, 6131062298875, 2213996101734400, 799006687503978595, 288434882201789270025, 104127350297268876278080, 37589924912686399826265625], "abvar_counts_str": "355 126025 47053120 17159690025 6131062298875 2213996101734400 799006687503978595 288434882201789270025 104127350297268876278080 37589924912686399826265625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.220513589303589, 0.779486410696411], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 348, 6860, 131668, 2476100, 47060358, 893871740, 16983178468, 322687697780, 6131058339948], "curve_counts_str": "20 348 6860 131668 2476100 47060358 893871740 16983178468 322687697780 6131058339948 ", "curves": ["y^2=15*x^6+14*x^5+x^4+3*x^3+14*x^2+8*x+6", "y^2=5*x^6+7*x^5+6*x^4+8*x^3+17*x^2+2*x+5", "y^2=10*x^6+14*x^5+12*x^4+16*x^3+15*x^2+4*x+10", "y^2=2*x^6+x^5+12*x^4+13*x^3+6*x^2+17*x+1", "y^2=4*x^6+2*x^5+5*x^4+7*x^3+12*x^2+15*x+2", "y^2=8*x^6+15*x^5+2*x^4+18*x^3+9*x^2+14*x+7", "y^2=7*x^6+6*x^5+3*x^4+8*x^3+14*x^2+12*x+16", "y^2=14*x^6+12*x^5+6*x^4+16*x^3+9*x^2+5*x+13", "y^2=3*x^6+12*x^5+8*x^4+7*x^3+13*x^2+13*x+13", "y^2=6*x^6+5*x^5+16*x^4+14*x^3+7*x^2+7*x+7", "y^2=6*x^6+10*x^5+13*x^4+13*x^3+15*x^2+14*x+18", "y^2=12*x^6+x^5+7*x^4+7*x^3+11*x^2+9*x+17", "y^2=12*x^6+10*x^5+18*x^4+8*x^3+x^2+12*x+7", "y^2=5*x^6+x^5+17*x^4+16*x^3+2*x^2+5*x+14", "y^2=11*x^6+16*x^5+15*x^4+18*x^3+6*x^2+17*x+8", "y^2=2*x^6+9*x^5+10*x^4+15*x^3+x^2+17*x+16", "y^2=15*x^6+13*x^5+8*x^4+16*x^3+16*x^2+14*x+6", "y^2=16*x^6+17*x^5+3*x^4+12*x^3+16*x^2+17*x+3", "y^2=4*x^6+6*x^5+11*x^4+9*x^3+13*x^2+15", "y^2=8*x^6+12*x^5+3*x^4+18*x^3+7*x^2+11", "y^2=2*x^6+x^5+14*x^4+5*x^3+3*x^2+18*x+6", "y^2=4*x^6+2*x^5+9*x^4+10*x^3+6*x^2+17*x+12", "y^2=18*x^6+x^5+x^4+12*x^3+16*x^2+6*x+17", "y^2=17*x^6+2*x^5+2*x^4+5*x^3+13*x^2+12*x+15", "y^2=9*x^6+9*x^5+5*x^4+5*x^3+13*x^2+4*x+5", "y^2=18*x^6+18*x^5+10*x^4+10*x^3+7*x^2+8*x+10", "y^2=12*x^6+7*x^5+16*x^4+16*x^3+5*x+17", "y^2=5*x^6+14*x^5+13*x^4+13*x^3+10*x+15", "y^2=x^6+3*x^5+6*x^4+8*x^3+7*x^2+5", "y^2=2*x^6+6*x^5+12*x^4+16*x^3+14*x^2+10"], "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": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 30, "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": 30, "label": "2.19.a_ah", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.24025.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 6], [1, 19, 1, 6]], "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, -45], "simple_distinct": ["2.19.a_ah"], "simple_factors": ["2.19.a_ahA"], "simple_multiplicities": [1], "singular_primes": ["2,-9*F^2+3*F-9", "3,-F+2*V-6"], "size": 36, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.24025.1", "splitting_polynomials": [[81, 0, 13, 0, 1]], "twist_count": 2, "twists": [["2.19.a_h", "2.130321.bzu_boppb", 4]], "weak_equivalence_count": 4, "zfv_index": 36, "zfv_index_factorization": [[2, 2], [3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 6, "zfv_plus_index_factorization": [[2, 1], [3, 1]], "zfv_plus_norm": 961, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-9*F^2+3*F-9", "3,-F+2*V-6"]}