# Stored data for abelian variety isogeny class 2.19.a_ao, downloaded from the LMFDB on 24 June 2026.
{"abvar_count": 348, "abvar_counts": [348, 121104, 47058300, 17121199104, 6131061550428, 2214483598890000, 799006686640636668, 288440868972945752064, 104127350298073533380700, 37589915735136591186983184], "abvar_counts_str": "348 121104 47058300 17121199104 6131061550428 2214483598890000 799006686640636668 288440868972945752064 104127350298073533380700 37589915735136591186983184 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.189949243271783, 0.810050756728217], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 334, 6860, 131374, 2476100, 47070718, 893871740, 16983530974, 322687697780, 6131056843054], "curve_counts_str": "20 334 6860 131374 2476100 47070718 893871740 16983530974 322687697780 6131056843054 ", "curves": ["y^2=14*x^6+15*x^5+9*x^4+18*x^2+3*x+17", "y^2=16*x^6+3*x^5+9*x^4+18*x^3+11*x^2+3*x+18", "y^2=13*x^6+6*x^5+18*x^4+17*x^3+3*x^2+6*x+17", "y^2=13*x^6+17*x^5+10*x^4+12*x^3+16*x^2+4*x+4", "y^2=18*x^6+7*x^5+13*x^4+14*x^2+x", "y^2=17*x^6+14*x^5+7*x^4+9*x^2+2*x", "y^2=8*x^6+3*x^5+3*x^3+17*x^2+11*x+12", "y^2=16*x^6+6*x^5+6*x^3+15*x^2+3*x+5", "y^2=18*x^6+x^5+16*x^4+2*x^3+13*x^2+4*x+11", "y^2=16*x^6+8*x^5+18*x^4+7*x^3+14*x^2+17*x+13", "y^2=13*x^6+16*x^5+17*x^4+14*x^3+9*x^2+15*x+7", "y^2=17*x^6+12*x^5+6*x^4+16*x^3+18*x^2+13*x+3", "y^2=4*x^5+2*x^4+7*x^3+3*x^2+x+15", "y^2=8*x^5+4*x^4+14*x^3+6*x^2+2*x+11", "y^2=9*x^6+17*x^5+3*x^4+8*x^3+5*x^2+6*x+4", "y^2=18*x^6+15*x^5+6*x^4+16*x^3+10*x^2+12*x+8", "y^2=6*x^6+12*x^5+13*x^4+18*x^3+x^2+13*x+10", "y^2=3*x^6+5*x^5+18*x^4+11*x^3+4*x^2+4*x+17", "y^2=9*x^6+x^5+17*x^4+17*x^3+12*x^2+17*x+13", "y^2=4*x^6+14*x^5+16*x^4+3*x^3+15*x^2+6*x+4", "y^2=8*x^6+9*x^5+13*x^4+6*x^3+11*x^2+12*x+8", "y^2=13*x^6+4*x^5+10*x^4+17*x^3+7*x^2+5*x+9"], "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": 5, "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": ["2.0.312.1"], "geometric_splitting_field": "2.0.312.1", "geometric_splitting_polynomials": [[78, 0, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 22, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 22, "label": "2.19.a_ao", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.97344.4"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, -14, 0, 361], "poly_str": "1 0 -14 0 361 ", "primitive_models": [], "q": 19, "real_poly": [1, 0, -52], "simple_distinct": ["2.19.a_ao"], "simple_factors": ["2.19.a_aoA"], "simple_multiplicities": [1], "singular_primes": ["2,F-4*V+5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.97344.4", "splitting_polynomials": [[87, -6, 7, -2, 1]], "twist_count": 2, "twists": [["2.19.a_o", "2.130321.bom_beowc", 4]], "weak_equivalence_count": 5, "zfv_index": 16, "zfv_index_factorization": [[2, 4]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 4, "zfv_plus_index_factorization": [[2, 2]], "zfv_plus_norm": 576, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F-4*V+5"]}