# Stored data for abelian variety isogeny class 2.19.a_bl, downloaded from the LMFDB on 14 March 2026.
{"abvar_count": 399, "abvar_counts": [399, 159201, 47056464, 16815605625, 6131068282479, 2214310804183296, 799006685713793319, 288436047941535755625, 104127350297602681851984, 37589998284419994938385441], "abvar_counts_str": "399 159201 47056464 16815605625 6131068282479 2214310804183296 799006685713793319 288436047941535755625 104127350297602681851984 37589998284419994938385441 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.463406802479836, 0.536593197520164], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 436, 6860, 129028, 2476100, 47067046, 893871740, 16983247108, 322687697780, 6131070307156], "curve_counts_str": "20 436 6860 129028 2476100 47067046 893871740 16983247108 322687697780 6131070307156 ", "curves": ["y^2=9*x^6+5*x^5+18*x^4+16*x^3+9*x^2+16*x+2", "y^2=18*x^6+10*x^5+17*x^4+13*x^3+18*x^2+13*x+4", "y^2=10*x^6+7*x^5+6*x^4+15*x^3+9*x^2+11*x+10", "y^2=x^6+14*x^5+12*x^4+11*x^3+18*x^2+3*x+1", "y^2=17*x^6+11*x^5+16*x^4+10*x^3+5*x^2+x+17", "y^2=15*x^6+3*x^5+13*x^4+x^3+10*x^2+2*x+15", "y^2=12*x^6+17*x^5+10*x^4+9*x^3+10*x^2+17*x+12", "y^2=5*x^6+15*x^5+x^4+18*x^3+x^2+15*x+5", "y^2=18*x^6+x^5+18*x^4+14*x^3+14*x^2+6*x+8", "y^2=17*x^6+2*x^5+17*x^4+9*x^3+9*x^2+12*x+16", "y^2=11*x^6+13*x^5+14*x^4+16*x^3+2*x^2+15*x+11", "y^2=3*x^6+7*x^5+9*x^4+13*x^3+4*x^2+11*x+3", "y^2=8*x^6+3*x^5+12*x^4+6*x^3+8*x^2+14*x+8", "y^2=16*x^6+6*x^5+5*x^4+12*x^3+16*x^2+9*x+16"], "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": 8, "g": 2, "galois_groups": ["2T1", "2T1"], "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 14, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 14, "label": "2.19.a_bl", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.3.1", "2.0.3.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [2, 3, 1, 2], [1, 7, 1, 6]], "poly": [1, 0, 37, 0, 361], "poly_str": "1 0 37 0 361 ", "primitive_models": [], "principal_polarization_count": 26, "q": 19, "real_poly": [1, 0, -1], "simple_distinct": ["1.19.ab", "1.19.b"], "simple_factors": ["1.19.abA", "1.19.bA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F^2+5*F+25", "5,-F^2+2*V-12", "5,13*F+11*V-13"], "size": 26, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.19.ac_bn", "2.361.cw_dcl", 2], ["2.19.c_bn", "2.361.cw_dcl", 2], ["2.19.ap_dq", "2.6859.a_pra", 3], ["2.19.aj_bu", "2.6859.a_pra", 3], ["2.19.ag_bf", "2.6859.a_pra", 3], ["2.19.a_aba", "2.6859.a_pra", 3], ["2.19.a_al", "2.6859.a_pra", 3], ["2.19.g_bf", "2.6859.a_pra", 3], ["2.19.j_bu", "2.6859.a_pra", 3], ["2.19.p_dq", "2.6859.a_pra", 3], ["2.19.a_abl", "2.130321.abxu_bmqvb", 4], ["2.19.aq_dy", "2.47045881.bfia_riynzy", 6], ["2.19.ao_dj", "2.47045881.bfia_riynzy", 6], ["2.19.ai_bt", "2.47045881.bfia_riynzy", 6], ["2.19.ah_be", "2.47045881.bfia_riynzy", 6], ["2.19.ab_as", "2.47045881.bfia_riynzy", 6], ["2.19.a_al", "2.47045881.bfia_riynzy", 6], ["2.19.b_as", "2.47045881.bfia_riynzy", 6], ["2.19.h_be", "2.47045881.bfia_riynzy", 6], ["2.19.i_bt", "2.47045881.bfia_riynzy", 6], ["2.19.o_dj", "2.47045881.bfia_riynzy", 6], ["2.19.q_dy", "2.47045881.bfia_riynzy", 6], ["2.19.a_l", "2.2213314919066161.adahkae_bhqfruozgyag", 12], ["2.19.a_ba", "2.2213314919066161.adahkae_bhqfruozgyag", 12]], "weak_equivalence_count": 8, "zfv_index": 100, "zfv_index_factorization": [[2, 2], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 5625, "zfv_singular_count": 6, "zfv_singular_primes": ["2,F^2+5*F+25", "5,-F^2+2*V-12", "5,13*F+11*V-13"]}