# Stored data for abelian variety isogeny class 2.19.ae_g, downloaded from the LMFDB on 11 September 2025.
{"abvar_count": 288, "abvar_counts": [288, 129024, 45559584, 17020846080, 6139978364448, 2213192742598656, 799068404717211168, 288449268959839518720, 104127331058903909592864, 37589992898409852999727104], "abvar_counts_str": "288 129024 45559584 17020846080 6139978364448 2213192742598656 799068404717211168 288449268959839518720 104127331058903909592864 37589992898409852999727104 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.130073469146503, 0.651731832911273], "center_dim": 4, "cohen_macaulay_max": 3, "curve_count": 16, "curve_counts": [16, 358, 6640, 130606, 2479696, 47043286, 893940784, 16984025566, 322687638160, 6131069428678], "curve_counts_str": "16 358 6640 130606 2479696 47043286 893940784 16984025566 322687638160 6131069428678 ", "curves": ["y^2=10*x^6+14*x^5+7*x^4+14*x^3+15*x^2+11", "y^2=11*x^6+x^5+8*x^4+17*x^3+10*x^2+2", "y^2=15*x^6+3*x^4+13*x^3+6*x^2+5*x+8", "y^2=9*x^6+11*x^5+13*x^3+9*x+4", "y^2=4*x^6+12*x^5+3*x^3+10*x^2+16*x", "y^2=x^5+12*x^4+13*x^2+15*x+16", "y^2=9*x^6+9*x^5+6*x^4+18*x^3+12*x^2+13*x+8", "y^2=16*x^6+x^5+5*x^4+9*x^3+11*x^2+9*x+14", "y^2=11*x^6+3*x^5+3*x^4+2*x^3+5*x^2+13*x+13", "y^2=12*x^6+12*x^5+9*x^4+2*x^3+14*x^2+3*x+15", "y^2=18*x^6+13*x^5+15*x^4+2*x^3+10*x^2+4*x+10", "y^2=2*x^5+16*x^4+16*x^3+5*x^2+16", "y^2=17*x^6+3*x^5+15*x^4+5*x^3+15*x^2+14*x", "y^2=9*x^6+7*x^5+3*x^4+17*x^3+7*x^2+8*x+13", "y^2=9*x^6+15*x^5+7*x^4+10*x^3+3*x^2+8*x+9", "y^2=10*x^6+12*x^5+17*x^4+14*x^3+13*x^2+17*x+9", "y^2=9*x^5+17*x^4+14*x^3+18*x^2+11*x+18", "y^2=12*x^6+18*x^5+17*x^4+5*x^3+17*x^2+18*x+12", "y^2=x^6+4*x^5+17*x^4+4*x^3+6*x^2+4*x+6", "y^2=15*x^6+7*x^5+15*x^4+4*x^2+14*x", "y^2=x^6+2*x^5+15*x^4+4*x^3+13*x^2+8*x", "y^2=9*x^6+12*x^5+7*x^4+16*x^3+7*x+6", "y^2=4*x^6+18*x^5+4*x^4+15*x^3+16*x^2+11*x+10", "y^2=7*x^6+2*x^5+9*x^4+4*x^3+9*x^2+2*x+7", "y^2=12*x^6+7*x^5+7*x^4+13*x^3+6*x^2+4*x+10", "y^2=9*x^6+4*x^5+9*x^4+5*x^3+11*x^2+6*x", "y^2=2*x^5+13*x^4+11*x^3+11*x^2+10*x+6", "y^2=2*x^6+6*x^5+10*x^4+13*x^3+12*x^2+3*x+4", "y^2=7*x^6+2*x^5+17*x^4+16*x^3+5*x^2+3*x+7", "y^2=4*x^6+3*x^5+6*x^4+7*x^3+15*x^2+9*x+2", "y^2=11*x^6+14*x^5+13*x^4+x^2+x", "y^2=3*x^6+9*x^5+5*x^4+x^3+5*x^2+13*x+6", "y^2=10*x^6+5*x^5+9*x^3+11*x+15", "y^2=11*x^6+11*x^4+13*x^3+8*x^2+3*x+4", "y^2=3*x^6+18*x^5+4*x^4+x^3+x^2+14*x+10", "y^2=13*x^6+14*x^5+7*x^4+12*x^3+5*x+15", "y^2=x^6+11*x^5+14*x^4+5*x^3+15*x^2+11*x+3", "y^2=10*x^6+15*x^5+15*x^4+8*x^3+14*x^2+12*x+9", "y^2=13*x^6+7*x^5+18*x^4+5*x^3+2*x^2+x", "y^2=14*x^6+5*x^5+2*x^4+10*x^3+x^2+6*x+7", "y^2=14*x^6+17*x^5+10*x^4+18*x^3+10*x^2+17*x+14", "y^2=10*x^5+5*x^3+17*x^2+9*x+6", "y^2=12*x^6+3*x^5+12*x^4+9*x^3+12*x^2+3*x+12", "y^2=10*x^6+18*x^5+8*x^4+11*x^3+8*x^2+18*x+10"], "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": 42, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.3.1", "2.0.15.1"], "geometric_splitting_field": "4.0.225.1", "geometric_splitting_polynomials": [[1, 1, 2, -1, 1]], "group_structure_count": 12, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 44, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 44, "label": "2.19.ae_g", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.3.1", "2.0.15.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -4, 6, -76, 361], "poly_str": "1 -4 6 -76 361 ", "primitive_models": [], "q": 19, "real_poly": [1, -4, -32], "simple_distinct": ["1.19.ai", "1.19.e"], "simple_factors": ["1.19.aiA", "1.19.eA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,F+5", "2,F+3"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.225.1", "splitting_polynomials": [[1, 1, 2, -1, 1]], "twist_count": 12, "twists": [["2.19.am_cs", "2.361.ae_fu", 2], ["2.19.e_g", "2.361.ae_fu", 2], ["2.19.m_cs", "2.361.ae_fu", 2], ["2.19.f_bq", "2.6859.aim_bhww", 3], ["2.19.l_co", "2.6859.aim_bhww", 3], ["2.19.al_co", "2.47045881.advw_advgrkc", 6], ["2.19.af_bq", "2.47045881.advw_advgrkc", 6], ["2.19.ad_k", "2.47045881.advw_advgrkc", 6], ["2.19.ad_bi", "2.47045881.advw_advgrkc", 6], ["2.19.d_k", "2.47045881.advw_advgrkc", 6], ["2.19.d_bi", "2.47045881.advw_advgrkc", 6]], "weak_equivalence_count": 72, "zfv_index": 576, "zfv_index_factorization": [[2, 6], [3, 2]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 720, "zfv_singular_count": 4, "zfv_singular_primes": ["3,F+5", "2,F+3"]}