# Stored data for abelian variety isogeny class 2.19.a_k, downloaded from the LMFDB on 14 January 2026.
{"abvar_count": 372, "abvar_counts": [372, 138384, 47036052, 17146331136, 6131071068852, 2212390187746704, 799006684071466452, 288437125539594240000, 104127350298348762476532, 37590032451314005724597904], "abvar_counts_str": "372 138384 47036052 17146331136 6131071068852 2212390187746704 799006684071466452 288437125539594240000 104127350298348762476532 37590032451314005724597904 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.292382009140157, 0.707617990859843], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 20, "curve_counts": [20, 382, 6860, 131566, 2476100, 47026222, 893871740, 16983310558, 322687697780, 6131075879902], "curve_counts_str": "20 382 6860 131566 2476100 47026222 893871740 16983310558 322687697780 6131075879902 ", "curves": ["y^2=16*x^6+5*x^5+9*x^4+10*x^3+6*x^2+3*x+16", "y^2=13*x^6+10*x^5+18*x^4+x^3+12*x^2+6*x+13", "y^2=14*x^6+11*x^4+3*x^3+15*x^2+16", "y^2=14*x^6+3*x^5+12*x^4+3*x^2+7*x+15", "y^2=9*x^6+6*x^5+5*x^4+6*x^2+14*x+11", "y^2=4*x^6+x^5+7*x^4+2*x^3+8*x^2+9*x+14", "y^2=8*x^6+2*x^5+14*x^4+4*x^3+16*x^2+18*x+9", "y^2=4*x^5+2*x^4+6*x^3+9*x^2+5*x", "y^2=7*x^6+8*x^5+8*x^4+5*x^3+14*x^2+2*x+2", "y^2=16*x^6+18*x^5+10*x^4+12*x^3+x^2+13*x+7", "y^2=x^6+16*x^5+5*x^4+7*x^3+13*x^2+x+8", "y^2=4*x^6+12*x^5+7*x^4+5*x^3+12*x^2+3*x+3", "y^2=8*x^6+5*x^5+14*x^4+10*x^3+5*x^2+6*x+6", "y^2=x^6+3*x^5+16*x^4+15*x^3+14*x^2+7*x+10", "y^2=16*x^6+5*x^5+2*x^3+2*x^2+10*x+16", "y^2=x^6+2*x^3+8", "y^2=6*x^6+3*x^5+2*x^4+13*x^3+4*x^2+12*x+10", "y^2=x^6+14*x^3+8", "y^2=2*x^6+9*x^5+x^4+18*x^3+12*x^2+3*x+17", "y^2=4*x^6+18*x^5+2*x^4+17*x^3+5*x^2+6*x+15", "y^2=4*x^5+4*x^4+6*x^3+14*x^2+11*x", "y^2=11*x^6+7*x^5+17*x^4+12*x^3+10*x^2+4*x+12", "y^2=16*x^6+6*x^5+x^4+9*x^3+x^2+2*x+6", "y^2=13*x^6+12*x^5+2*x^4+18*x^3+2*x^2+4*x+12", "y^2=16*x^6+14*x^5+2*x^4+6*x^3+6*x^2+12*x+14", "y^2=14*x^6+4*x^5+11*x^4+18*x^3+13*x^2+7*x+16", "y^2=11*x^6+11*x^5+11*x^4+6*x^3+15*x^2+17*x+18", "y^2=7*x^6+x^5+x^4+4*x^3+3*x^2+9*x+18", "y^2=3*x^6+2*x^5+16*x^4+11*x^3+8*x^2+13*x", "y^2=6*x^6+4*x^5+13*x^4+3*x^3+16*x^2+7*x", "y^2=18*x^5+3*x^4+18*x^3+15*x^2+6*x+4", "y^2=17*x^5+6*x^4+17*x^3+11*x^2+12*x+8", "y^2=11*x^6+16*x^5+11*x^4+4*x^3+5*x^2+4*x+4", "y^2=x^6+9*x^5+9*x^4+4*x^3+3*x^2+11*x+13", "y^2=12*x^5+18*x^4+6*x^3+17*x^2+10*x", "y^2=7*x^6+11*x^5+7*x^4+10*x^3+13*x^2+13*x+8", "y^2=14*x^6+3*x^5+14*x^4+x^3+7*x^2+7*x+16", "y^2=17*x^6+x^5+6*x^4+8*x^3+14*x^2+16*x+14", "y^2=13*x^6+6*x^5+7*x^4+17*x^3+3*x^2+4*x+5", "y^2=7*x^6+12*x^5+14*x^4+15*x^3+6*x^2+8*x+10", "y^2=18*x^6+2*x^5+6*x^4+16*x^3+18*x^2+18*x+11", "y^2=7*x^6+4*x^4+9*x^3+3*x^2+6*x+4", "y^2=14*x^6+8*x^4+18*x^3+6*x^2+12*x+8", "y^2=14*x^6+13*x^5+16*x^4+2*x^3+18*x^2+12*x+16", "y^2=8*x^6+14*x^5+8*x^4+4*x^3+x^2+2*x+11", "y^2=12*x^6+10*x^5+3*x^4+18*x^3+14*x^2+2*x+13", "y^2=5*x^6+x^5+6*x^4+17*x^3+9*x^2+4*x+7", "y^2=13*x^6+x^5+9*x^4+7*x^3+14*x^2+5*x+4", "y^2=9*x^5+11*x^4+14*x^3+11*x^2+17*x", "y^2=18*x^5+3*x^4+9*x^3+3*x^2+15*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": 7, "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": ["2.0.84.1"], "geometric_splitting_field": "2.0.84.1", "geometric_splitting_polynomials": [[21, 0, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 50, "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": 50, "label": "2.19.a_k", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.7056.3"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [1, 3, 2, 2], [1, 7, 1, 4], [1, 19, 1, 4]], "poly": [1, 0, 10, 0, 361], "poly_str": "1 0 10 0 361 ", "primitive_models": [], "principal_polarization_count": 64, "q": 19, "real_poly": [1, 0, -28], "simple_distinct": ["2.19.a_k"], "simple_factors": ["2.19.a_kA"], "simple_multiplicities": [1], "singular_primes": ["2,7*F^2-F"], "size": 80, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.7056.3", "splitting_polynomials": [[49, 0, 7, 0, 1]], "twist_count": 4, "twists": [["2.19.am_cp", "2.6859.a_aooc", 3], ["2.19.m_cp", "2.6859.a_aooc", 3], ["2.19.a_ak", "2.130321.bvw_bkvww", 4], ["2.19.am_cp", "2.47045881.abdce_qbjfec", 6], ["2.19.m_cp", "2.47045881.abdce_qbjfec", 6]], "weak_equivalence_count": 7, "zfv_index": 64, "zfv_index_factorization": [[2, 6]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 32, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 2304, "zfv_singular_count": 2, "zfv_singular_primes": ["2,7*F^2-F"]}