# Stored data for abelian variety isogeny class 2.19.a_n, downloaded from the LMFDB on 15 April 2026.
{"abvar_count": 375, "abvar_counts": [375, 140625, 47034000, 17128265625, 6131071134375, 2212197156000000, 799006684634613375, 288439879410444515625, 104127350297910715386000, 37590033254766349306640625], "abvar_counts_str": "375 140625 47034000 17128265625 6131071134375 2212197156000000 799006684634613375 288439879410444515625 104127350297910715386000 37590033254766349306640625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.30556997246711, 0.69443002753289], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 388, 6860, 131428, 2476100, 47022118, 893871740, 16983472708, 322687697780, 6131076010948], "curve_counts_str": "20 388 6860 131428 2476100 47022118 893871740 16983472708 322687697780 6131076010948 ", "curves": ["y^2=x^6+9*x^5+17*x^4+13*x^3+11*x^2+16*x+8", "y^2=2*x^6+18*x^5+15*x^4+7*x^3+3*x^2+13*x+16", "y^2=3*x^6+13*x^5+4*x^4+15*x^3+5*x^2+12*x+2", "y^2=6*x^6+7*x^5+8*x^4+11*x^3+10*x^2+5*x+4", "y^2=4*x^6+14*x^5+8*x^4+10*x^3+9*x^2+16*x+9", "y^2=8*x^6+9*x^5+16*x^4+x^3+18*x^2+13*x+18", "y^2=5*x^6+17*x^5+8*x^4+3*x^3+17*x^2+7*x+2", "y^2=11*x^6+18*x^5+10*x^4+3*x^3+6*x^2+12*x+7", "y^2=3*x^6+17*x^5+x^4+6*x^3+12*x^2+5*x+14", "y^2=9*x^6+7*x^5+15*x^4+10*x^3+16*x^2+14*x+16", "y^2=18*x^6+14*x^5+11*x^4+x^3+13*x^2+9*x+13", "y^2=12*x^6+4*x^5+6*x^4+5*x^3+4*x^2+11*x+1", "y^2=5*x^6+8*x^5+12*x^4+10*x^3+8*x^2+3*x+2", "y^2=8*x^6+16*x^5+10*x^4+6*x^3+7*x^2+x+7", "y^2=5*x^6+17*x^5+9*x^4+2*x^3+14*x^2+9*x+3", "y^2=13*x^6+15*x^5+5*x^4+18*x^3+x^2+x+13", "y^2=7*x^6+11*x^5+10*x^4+17*x^3+2*x^2+2*x+7", "y^2=10*x^6+6*x^5+11*x^4+14*x^3+7*x^2+4*x+10", "y^2=x^6+12*x^5+3*x^4+9*x^3+14*x^2+8*x+1", "y^2=7*x^6+6*x^5+x^3+5*x+18", "y^2=10*x^6+11*x^5+7*x^4+11*x^3+11*x^2+7*x+10", "y^2=x^6+3*x^5+14*x^4+3*x^3+3*x^2+14*x+1", "y^2=7*x^6+11*x^5+8*x^4+9*x^3+5*x^2+6*x+5", "y^2=14*x^6+3*x^5+16*x^4+18*x^3+10*x^2+12*x+10", "y^2=6*x^6+10*x^5+13*x^4+6*x^3+5*x^2+18*x+8", "y^2=12*x^6+x^5+7*x^4+12*x^3+10*x^2+17*x+16", "y^2=6*x^6+x^5+8*x^4+15*x^3+x^2+3*x+9", "y^2=12*x^6+2*x^5+16*x^4+11*x^3+2*x^2+6*x+18", "y^2=8*x^6+3*x^5+11*x^4+8*x^3+15*x^2+12*x+12", "y^2=16*x^6+6*x^5+3*x^4+16*x^3+11*x^2+5*x+5", "y^2=12*x^6+16*x^5+17*x^4+10*x^3+15*x^2+15*x+1", "y^2=5*x^6+13*x^5+15*x^4+x^3+11*x^2+11*x+2", "y^2=2*x^6+4*x^5+7*x^4+18*x^3+4*x^2+17*x+13", "y^2=4*x^6+8*x^5+14*x^4+17*x^3+8*x^2+15*x+7", "y^2=11*x^6+7*x^5+12*x^4+3*x^3+8*x^2+6", "y^2=3*x^6+14*x^5+5*x^4+6*x^3+16*x^2+12", "y^2=4*x^6+18*x^5+5*x^4+17*x^3+16*x^2+8*x+4", "y^2=8*x^6+17*x^5+10*x^4+15*x^3+13*x^2+16*x+8"], "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": ["2.0.51.1"], "geometric_splitting_field": "2.0.51.1", "geometric_splitting_polynomials": [[13, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 38, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 38, "label": "2.19.a_n", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [5], "number_fields": ["2.0.51.1", "2.0.51.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 4], [2, 3, 1, 4], [1, 11, 1, 12]], "poly": [1, 0, 13, 0, 361], "poly_str": "1 0 13 0 361 ", "primitive_models": [], "principal_polarization_count": 48, "q": 19, "real_poly": [1, 0, -25], "simple_distinct": ["1.19.af", "1.19.f"], "simple_factors": ["1.19.afA", "1.19.fA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,-F^2+7*V-8", "5,2*F+2", "5,-V-1"], "size": 208, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.51.1", "splitting_polynomials": [[13, -1, 1]], "twist_count": 6, "twists": [["2.19.ak_cl", "2.361.ba_bih", 2], ["2.19.k_cl", "2.361.ba_bih", 2], ["2.19.a_an", "2.130321.bqo_bgfyp", 4], ["2.19.af_g", "2.47045881.abjea_tuwbzy", 6], ["2.19.f_g", "2.47045881.abjea_tuwbzy", 6]], "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": 96, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2601, "zfv_singular_count": 6, "zfv_singular_primes": ["2,-F^2+7*V-8", "5,2*F+2", "5,-V-1"]}