# Stored data for abelian variety isogeny class 2.19.a_abb, downloaded from the LMFDB on 09 February 2026.
{"abvar_count": 335, "abvar_counts": [335, 112225, 47055440, 16981999225, 6131069843375, 2214214433593600, 799006684562375015, 288450265264784613225, 104127350297435422510160, 37590017424342347031390625], "abvar_counts_str": "335 112225 47055440 16981999225 6131069843375 2214214433593600 799006684562375015 288450265264784613225 104127350297435422510160 37590017424342347031390625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.124228461179968, 0.875771538820032], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 308, 6860, 130308, 2476100, 47064998, 893871740, 16984084228, 322687697780, 6131073428948], "curve_counts_str": "20 308 6860 130308 2476100 47064998 893871740 16984084228 322687697780 6131073428948 ", "curves": ["y^2=2*x^6+6*x^5+18*x^4+5*x^3+5*x^2+17*x+16", "y^2=16*x^6+10*x^5+5*x^4+14*x^3+14*x+16", "y^2=13*x^6+x^5+10*x^4+9*x^3+9*x+13", "y^2=16*x^6+15*x^5+6*x^4+4*x^3+7*x^2+5", "y^2=13*x^6+11*x^5+12*x^4+8*x^3+14*x^2+10", "y^2=4*x^6+18*x^4+2*x^3+7*x^2+15"], "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": ["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": ["2.0.715.1"], "geometric_splitting_field": "2.0.715.1", "geometric_splitting_polynomials": [[179, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 6, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 6, "label": "2.19.a_abb", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.511225.3"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 6], [1, 5, 2, 6]], "poly": [1, 0, -27, 0, 361], "poly_str": "1 0 -27 0 361 ", "primitive_models": [], "principal_polarization_count": 8, "q": 19, "real_poly": [1, 0, -65], "simple_distinct": ["2.19.a_abb"], "simple_factors": ["2.19.a_abbA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2+3*F-3"], "size": 16, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.511225.3", "splitting_polynomials": [[361, 0, -27, 0, 1]], "twist_count": 2, "twists": [["2.19.a_bb", "2.130321.ao_ovqp", 4]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 121, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2+3*F-3"]}