# Stored data for abelian variety isogeny class 2.19.b_k, downloaded from the LMFDB on 27 March 2026.
{"abvar_count": 392, "abvar_counts": [392, 137984, 47229728, 17141476352, 6125602539672, 2212503434645504, 799012317168186296, 288437549210690367488, 104127766489845091194656, 37590016950489449099453184], "abvar_counts_str": "392 137984 47229728 17141476352 6125602539672 2212503434645504 799012317168186296 288437549210690367488 104127766489845091194656 37590016950489449099453184 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.313740088325435, 0.732436694521959], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 21, "curve_counts": [21, 381, 6888, 131529, 2473891, 47028630, 893878041, 16983335505, 322688987544, 6131073351661], "curve_counts_str": "21 381 6888 131529 2473891 47028630 893878041 16983335505 322688987544 6131073351661 ", "curves": ["y^2=18*x^6+18*x^5+9*x^4+12*x^3+9*x^2+17*x+4", "y^2=10*x^5+10*x^4+3*x^3+14*x^2+x+5", "y^2=7*x^6+13*x^5+4*x^4+14*x^3+8*x^2+7", "y^2=3*x^6+11*x^5+15*x^4+7*x^3+8*x^2+12*x+16", "y^2=5*x^6+3*x^5+3*x^4+x^3+12*x^2+4*x+8", "y^2=11*x^6+16*x^5+x^4+2*x^3+x^2+14*x+3", "y^2=18*x^6+12*x^5+5*x^4+13*x^3+12*x^2+12*x+2", "y^2=9*x^6+11*x^5+16*x^4+10*x^3+11*x^2+7*x+11", "y^2=4*x^6+9*x^5+10*x^4+6*x^3+9*x^2+5*x", "y^2=4*x^6+x^5+8*x^3+8*x^2+1", "y^2=13*x^6+6*x^5+16*x^4+6*x^3+4*x^2+14*x+18", "y^2=10*x^6+4*x^5+10*x^4+11*x^3+3*x^2+4*x+15", "y^2=4*x^6+2*x^5+13*x^4+3*x^3+7*x^2+3*x+4", "y^2=12*x^6+10*x^5+5*x^4+16*x^3+18*x^2+7*x+5", "y^2=14*x^6+x^5+14*x^4+5*x^3+9*x^2+15*x+10", "y^2=3*x^6+18*x^5+13*x^4+9*x^3+17*x^2+5*x+5", "y^2=8*x^6+4*x^5+x^3+10*x^2+8*x+4", "y^2=11*x^6+5*x^5+11*x^4+2*x^3+8*x^2+6*x+3", "y^2=12*x^5+6*x^4+12*x^2+13*x+4", "y^2=x^6+13*x^5+9*x^4+9*x^3+17*x^2+18*x+17", "y^2=14*x^6+9*x^5+8*x^3+18*x^2+11*x+11", "y^2=17*x^6+5*x^5+17*x^4+11*x^3+14*x^2+3*x+7", "y^2=16*x^6+16*x^5+9*x^4+15*x^3+4*x^2+9*x+7", "y^2=3*x^6+17*x^5+12*x^4+5*x^3+7*x^2+4*x+9", "y^2=13*x^5+10*x^4+18*x^2+8*x+16", "y^2=9*x^6+12*x^5+7*x^4+11*x^3+7*x^2+2*x+12", "y^2=8*x^6+10*x^5+12*x^4+6*x^3+18*x^2+6*x", "y^2=16*x^6+6*x^5+10*x^4+8*x^3+13*x^2+6*x+11", "y^2=16*x^6+10*x^5+14*x^4+11*x^3+14*x^2+10*x+2", "y^2=9*x^6+10*x^5+5*x^2+4*x+17", "y^2=11*x^6+4*x^5+18*x^4+7*x^3+11*x^2+18*x+1", "y^2=3*x^6+18*x^5+16*x^4+8*x^3+18*x+1", "y^2=7*x^6+10*x^5+7*x^4+8*x^3+13*x^2+18*x+4", "y^2=12*x^6+17*x^5+12*x^4+8*x^3+8*x^2+17*x+3", "y^2=7*x^6+14*x^5+4*x^4+2*x^3+15*x^2+14*x+7", "y^2=7*x^6+4*x^5+15*x^4+4*x^3+14*x^2+5*x+18", "y^2=12*x^6+18*x^5+9*x^4+12*x^3+16*x^2+18*x", "y^2=4*x^6+15*x^5+16*x^4+18*x^2+14*x+10", "y^2=15*x^6+16*x^5+6*x^4+15*x^3+11*x^2+15*x+17", "y^2=12*x^6+18*x^5+x^4+2*x^3+2*x^2+x+16", "y^2=13*x^6+2*x^5+x^4+9*x^3+10*x^2+7*x+7", "y^2=3*x^6+12*x^5+9*x^4+3*x^3+18*x^2+16*x"], "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": ["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": ["4.0.7112333.1"], "geometric_splitting_field": "4.0.7112333.1", "geometric_splitting_polynomials": [[361, -19, 10, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 42, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 42, "label": "2.19.b_k", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.7112333.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 21]], "poly": [1, 1, 10, 19, 361], "poly_str": "1 1 10 19 361 ", "primitive_models": [], "principal_polarization_count": 42, "q": 19, "real_poly": [1, 1, -28], "simple_distinct": ["2.19.b_k"], "simple_factors": ["2.19.b_kA"], "simple_multiplicities": [1], "singular_primes": ["2,-F-3"], "size": 42, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.7112333.1", "splitting_polynomials": [[361, -19, 10, -1, 1]], "twist_count": 2, "twists": [["2.19.ab_k", "2.361.t_bee", 2]], "weak_equivalence_count": 2, "zfv_index": 2, "zfv_index_factorization": [[2, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 21, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2228, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F-3"]}