# Stored data for abelian variety isogeny class 2.49.au_hg, downloaded from the LMFDB on 15 May 2024.
{"label": "2.49.au_hg", "g": 2, "p": 7, "q": 49, "poly": [1, -20, 188, -980, 2401], "poly_str": "1 -20 188 -980 2401 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.11067279977424, 0.337577521471145], "angle_rank": 2, "number_fields": ["4.0.5433600.1"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [1590, 5708100, 13881286710, 33240526707600, 79788566331849750, 191579590025849204100, 459986919375032320916310, 1104428258654316787741593600, 2651731107753872205214939352790, 6366805820626796818077911187562500], "abvar_counts_str": "1590 5708100 13881286710 33240526707600 79788566331849750 191579590025849204100 459986919375032320916310 1104428258654316787741593600 2651731107753872205214939352790 6366805820626796818077911187562500 ", "abvar_count": 1590, "curve_counts": [30, 2378, 117990, 5766118, 282462150, 13841168618, 678223637310, 33232948154878, 1628413758738270, 79792267046027498], "curve_counts_str": "30 2378 117990 5766118 282462150 13841168618 678223637310 33232948154878 1628413758738270 79792267046027498 ", "curve_count": 30, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.5433600.1"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.49.u_hg", "2.2401.ay_bkk", 2]], "twist_count": 2, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": true, "is_geometrically_simple": true, "simple_distinct": ["2.49.au_hg"], "simple_multiplicities": [1], "simple_factors": ["2.49.au_hgA"], "dim1_factors": 0, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 0, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 0, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -20, 90], "jacobian_count": 16, "curves": ["y^2=(a+1)*x^6+(2*a+5)*x^5+x^4+(6*a+1)*x^3+(a+1)*x^2+(4*a+3)*x+a+1", "y^2=3*x^6+(4*a+1)*x^5+(6*a+6)*x^4+(3*a+3)*x^3+2*a*x^2+(a+1)*x+4*a+4", "y^2=(4*a+1)*x^6+(6*a+2)*x^5+(6*a+2)*x^4+(a+5)*x^3+(3*a+3)*x^2+(5*a+4)*x+2*a+2", "y^2=(a+5)*x^6+a*x^5+(4*a+5)*x^4+6*a*x^3+a*x^2+(3*a+6)*x", "y^2=(5*a+6)*x^6+2*a*x^5+(5*a+2)*x^4+(6*a+2)*x^3+5*x^2+3*a*x+2*a+6", "y^2=(3*a+1)*x^6+(5*a+2)*x^5+(4*a+5)*x^4+(2*a+1)*x^3+(4*a+2)*x^2+3*x+6*a+1", "y^2=(4*a+1)*x^6+(2*a+1)*x^5+(a+3)*x^4+6*x^3+(5*a+2)*x^2+3*x+4*a+1", "y^2=(3*a+3)*x^6+6*a*x^5+(4*a+3)*x^4+5*a*x^3+(6*a+3)*x^2+(4*a+5)*x+2*a+4", "y^2=(3*a+2)*x^6+(2*a+5)*x^5+(6*a+5)*x^4+5*a*x^3+(5*a+2)*x^2+(6*a+3)*x+6", "y^2=(a+1)*x^6+(3*a+6)*x^5+(6*a+2)*x^4+(a+6)*x^3+3*a*x^2+x+4*a+1", "y^2=(5*a+4)*x^6+(3*a+3)*x^5+(2*a+5)*x^4+(5*a+5)*x^3+(3*a+2)*x^2+(2*a+4)*x+5*a", "y^2=6*a*x^6+2*x^4+(2*a+5)*x^3+(2*a+4)*x^2+(3*a+2)*x+5*a", "y^2=(5*a+4)*x^6+(a+5)*x^5+(a+5)*x^4+2*x^3+(4*a+1)*x^2+(6*a+5)*x+a+5", "y^2=(6*a+1)*x^6+(a+6)*x^5+2*x^4+5*x^3+(a+2)*x^2+(5*a+2)*x+a+6", "y^2=(5*a+1)*x^5+(2*a+4)*x^4+2*a*x^3+(a+3)*x^2+(2*a+1)*x+2*a", "y^2=(5*a+3)*x^6+(a+3)*x^5+(2*a+1)*x^4+(4*a+3)*x^3+(2*a+4)*x^2+3*a*x+3*a+1"], "hyp_count": 16, "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_index": 1, "zfv_index_factorization": [], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3396, "geometric_splitting_field": "4.0.5433600.1", "splitting_field": "4.0.5433600.1", "geometric_splitting_polynomials": [[326, -100, 38, 0, 1]], "splitting_polynomials": [[326, -100, 38, 0, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 32, "principal_polarization_count": 16, "pic_prime_gens": [[1, 2, 1, 4], [1, 3, 1, 4], [1, 5, 1, 8]]}