# Stored data for abelian variety isogeny class 2.19.ac_w, downloaded from the LMFDB on 22 September 2025.
{"abvar_count": 344, "abvar_counts": [344, 145856, 47104952, 17049982976, 6138593594424, 2212413703507904, 798926721871044824, 288444379794389172224, 104127509276986662775832, 37589977505266908957245376], "abvar_counts_str": "344 145856 47104952 17049982976 6138593594424 2212413703507904 798926721871044824 288444379794389172224 104127509276986662775832 37589977505266908957245376 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.300049074133691, 0.616624673873194], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 18, "curve_counts": [18, 402, 6870, 130830, 2479138, 47026722, 893782278, 16983737694, 322688190450, 6131066918002], "curve_counts_str": "18 402 6870 130830 2479138 47026722 893782278 16983737694 322688190450 6131066918002 ", "curves": ["y^2=6*x^6+6*x^5+x^4+15*x^3+14*x^2+10*x+15", "y^2=15*x^6+6*x^5+17*x^4+12*x^3+16*x^2+2*x+6", "y^2=16*x^6+8*x^5+18*x^4+10*x^3+17*x^2+14*x+15", "y^2=5*x^5+12*x^3+18*x^2+2*x+3", "y^2=14*x^6+7*x^5+8*x^4+13*x^3+4*x^2+17*x+2", "y^2=2*x^6+13*x^5+18*x^4+x^3+2*x^2+3*x+1", "y^2=18*x^6+16*x^5+17*x^4+2*x^3+18*x^2+17*x+14", "y^2=10*x^6+5*x^5+x^4+3*x^3+2*x^2+9*x+17", "y^2=4*x^6+3*x^5+10*x^4+13*x^3+17*x^2+3*x+10", "y^2=7*x^6+3*x^5+18*x^4+16*x^3+11*x^2+6*x+3", "y^2=8*x^6+12*x^5+11*x^4+3*x^3+16*x^2+11*x+1", "y^2=13*x^6+5*x^5+12*x^3+13*x^2+13*x+10", "y^2=8*x^6+11*x^5+14*x^4+7*x^3+6*x^2+15*x+9", "y^2=9*x^6+14*x^5+14*x^4+13*x^3+13*x+8", "y^2=11*x^6+14*x^5+16*x^3+x^2+4*x+4", "y^2=13*x^6+10*x^5+15*x^4+8*x^3+11*x^2+x+8", "y^2=2*x^6+4*x^5+3*x^4+5*x^3+10*x^2+14", "y^2=15*x^5+17*x^4+16*x^2+13*x+16", "y^2=12*x^6+4*x^5+7*x^4+4*x^3+8*x^2+17*x+17", "y^2=2*x^6+17*x^5+17*x^4+x^3+9*x^2+8*x+12", "y^2=17*x^5+2*x^4+9*x^3+2*x^2+17*x+13", "y^2=11*x^6+4*x^5+11*x^4+14*x^3+x^2+x+3", "y^2=2*x^6+15*x^5+15*x^4+5*x^3+6*x^2+4*x+8", "y^2=11*x^6+6*x^5+5*x^4+10*x^3+14*x^2+10*x+6", "y^2=12*x^6+12*x^5+17*x^4+8*x^3+18*x^2+14*x+16", "y^2=5*x^6+13*x^5+18*x^4+4*x^3+5*x^2+17*x+4", "y^2=10*x^6+5*x^5+14*x^4+13*x^3+13*x^2+11*x+4", "y^2=10*x^6+6*x^5+2*x^4+15*x^3+14*x^2+2*x+8", "y^2=4*x^6+10*x^5+13*x^4+4*x^3+6*x^2+4*x+14", "y^2=11*x^6+15*x^5+8*x^4+x^3+15*x^2+18*x+7", "y^2=4*x^6+2*x^5+12*x^4+10*x^3+4*x^2+9*x+12", "y^2=5*x^6+16*x^5+2*x^4+7*x^3+6*x^2+17*x+11", "y^2=15*x^6+3*x^5+16*x^4+9*x^3+2*x^2+7*x+5", "y^2=11*x^6+8*x^5+16*x^4+17*x^3+17*x^2+6*x+18", "y^2=18*x^6+10*x^5+6*x^4+16*x^3+13*x^2+6*x+16", "y^2=18*x^6+2*x^5+5*x^4+13*x^3+15*x^2+7*x+14", "y^2=15*x^6+x^5+6*x^4+7*x^3+6*x^2+10*x", "y^2=8*x^6+15*x^5+13*x^4+x^3+x^2+17*x+18", "y^2=12*x^6+18*x^5+9*x^4+15*x^3+18*x^2+6*x+18", "y^2=3*x^6+7*x^5+13*x^4+7*x^3+16*x^2+2*x+3"], "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": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T3"], "geometric_number_fields": ["4.0.238136.1"], "geometric_splitting_field": "4.0.238136.1", "geometric_splitting_polynomials": [[206, 0, 29, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 40, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 40, "label": "2.19.ac_w", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.238136.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 13, 1, 4], [1, 19, 1, 12]], "poly": [1, -2, 22, -38, 361], "poly_str": "1 -2 22 -38 361 ", "primitive_models": [], "principal_polarization_count": 40, "q": 19, "real_poly": [1, -2, -16], "simple_distinct": ["2.19.ac_w"], "simple_factors": ["2.19.ac_wA"], "simple_multiplicities": [1], "singular_primes": ["2,F+2*V+1"], "size": 64, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.238136.1", "splitting_polynomials": [[206, 0, 29, 0, 1]], "twist_count": 2, "twists": [["2.19.c_w", "2.361.bo_boo", 2]], "weak_equivalence_count": 5, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 24, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 3296, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F+2*V+1"]}