# Stored data for abelian variety isogeny class 3.19.am_dp_ars, downloaded from the LMFDB on 11 March 2026.
{"abvar_count": 3916, "abvar_counts": [3916, 52959984, 334215683956, 2222164492171008, 15198359773327480156, 104150603793811110150384, 714165728388254978301997828, 4898614815629244646871959191552, 33600554402655542194866574999918828, 230466828417665592086026888165424394864], "abvar_counts_str": "3916 52959984 334215683956 2222164492171008 15198359773327480156 104150603793811110150384 714165728388254978301997828 4898614815629244646871959191552 33600554402655542194866574999918828 230466828417665592086026888165424394864 ", "angle_corank": 0, "angle_rank": 3, "angles": [0.217030023491845, 0.30038091355452, 0.495782070626515], "center_dim": 6, "curve_count": 8, "curve_counts": [8, 404, 7100, 130844, 2478908, 47056388, 893816960, 16983049532, 322687116368, 6131071858244], "curve_counts_str": "8 404 7100 130844 2478908 47056388 893816960 16983049532 322687116368 6131071858244 ", "curves": ["y^2=18*x^8+x^7+4*x^6+17*x^5+11*x^4+10*x^3+18*x^2+4*x+12", "y^2=18*x^8+10*x^7+9*x^6+7*x^5+6*x^4+13*x^3+2*x^2+10*x+15", "y^2=18*x^8+13*x^7+8*x^6+12*x^5+15*x^4+8*x^3+5*x^2+13*x+18", "y^2=18*x^8+17*x^7+16*x^6+12*x^5+4*x^4+6*x^3+3*x^2+18*x+2", "y^2=18*x^8+x^7+4*x^6+3*x^5+x^4+13*x^3+3*x^2+2*x+14", "y^2=18*x^8+4*x^7+16*x^6+12*x^5+x^4+2*x^3+6*x^2+5*x+15", "y^2=18*x^8+2*x^7+3*x^6+17*x^5+18*x^4+3*x^3+x^2+15*x+13", "y^2=18*x^8+15*x^7+17*x^6+12*x^4+18*x^3+9*x^2+10*x+6", "y^2=18*x^8+x^7+8*x^6+4*x^5+2*x^4+10*x^3+12*x^2+9*x+14", "y^2=18*x^8+5*x^7+7*x^6+4*x^4+13*x^3+15*x^2+6*x+14", "y^2=18*x^8+2*x^6+7*x^5+8*x^4+15*x^3+3*x^2+18*x+17", "y^2=x^8+11*x^7+14*x^6+x^4+12*x^3+14*x^2+14*x+3", "y^2=18*x^8+11*x^7+13*x^6+13*x^5+17*x^4+17*x^3+9*x^2+14*x+10", "y^2=18*x^8+x^7+8*x^6+3*x^5+7*x^4+13*x^3+17*x^2+16*x+15", "y^2=18*x^8+14*x^7+8*x^6+18*x^5+2*x^4+13*x^3+8*x^2+15*x+13", "y^2=x^8+16*x^7+18*x^6+12*x^5+6*x^4+x^3+3*x^2+11*x+3", "y^2=18*x^8+13*x^7+x^6+18*x^5+x^4+7*x^3+13*x+8", "y^2=18*x^8+16*x^7+2*x^6+3*x^5+11*x^3+5*x^2+8*x+15", "y^2=18*x^8+6*x^7+5*x^6+5*x^5+16*x^4+14*x^3+18*x^2+2*x+2", "y^2=18*x^8+15*x^7+2*x^6+10*x^5+16*x^4+7*x^3+4*x^2+16*x+1", "y^2=x^8+14*x^6+11*x^5+17*x^4+15*x^3+3*x^2+18*x+12", "y^2=x^8+x^7+9*x^6+2*x^5+7*x^4+16*x^3+11*x^2+17*x+3", "y^2=x^8+9*x^7+3*x^6+7*x^5+8*x^4+14*x^3+3*x^2+x+5"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 1, "dim3_factors": 1, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 3, "galois_groups": ["6T11"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 1, "geom_dim3_factors": 1, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 6, "geometric_extension_degree": 1, "geometric_galois_groups": ["6T11"], "geometric_number_fields": ["6.0.16329926592.1"], "geometric_splitting_field": "6.0.16329926592.1", "geometric_splitting_polynomials": [[2751, -576, 519, -36, 33, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 23, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "label": "3.19.am_dp_ars", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 4, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["6.0.16329926592.1"], "p": 19, "p_rank": 3, "p_rank_deficit": 0, "poly": [1, -12, 93, -460, 1767, -4332, 6859], "poly_str": "1 -12 93 -460 1767 -4332 6859 ", "primitive_models": [], "q": 19, "real_poly": [1, -12, 36, -4], "simple_distinct": ["3.19.am_dp_ars"], "simple_factors": ["3.19.am_dp_arsA"], "simple_multiplicities": [1], "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "splitting_field": "6.0.16329926592.1", "splitting_polynomials": [[2751, -576, 519, -36, 33, 0, 1]], "twist_count": 2, "twists": [["3.19.m_dp_rs", "3.361.bq_brz_bnrg", 2]]}