# Stored data for abelian variety isogeny class 2.43.at_gs, downloaded from the LMFDB on 09 May 2024.
{"label": "2.43.at_gs", "g": 2, "p": 43, "q": 43, "poly": [1, -19, 174, -817, 1849], "poly_str": "1 -19 174 -817 1849 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.183291501244178, 0.291171725172361], "angle_rank": 2, "number_fields": ["2.0.51.1", "2.0.3.1"], "galois_groups": ["2T1", "2T1"], "center_dim": 4, "abvar_counts": [1188, 3397680, 6369908688, 11707657790400, 21615418248855948, 39959882914299828480, 73885254522904205040924, 136613993349266267695660800, 252599331698176926793972788432, 467056168390046821057351705940400], "abvar_counts_str": "1188 3397680 6369908688 11707657790400 21615418248855948 39959882914299828480 73885254522904205040924 136613993349266267695660800 252599331698176926793972788432 467056168390046821057351705940400 ", "abvar_count": 1188, "curve_counts": [25, 1837, 80116, 3424489, 147035215, 6321402934, 271818232837, 11688197507281, 502592608205548, 21611482341632557], "curve_counts_str": "25 1837 80116 3424489 147035215 6321402934 271818232837 11688197507281 502592608205548 21611482341632557 ", "curve_count": 25, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["2.0.51.1", "2.0.3.1"], "geometric_galois_groups": ["2T1", "2T1"], "primitive_models": [], "is_primitive": true, "twists": [["2.43.ad_ac", "2.1849.an_eiq", 2], ["2.43.d_ac", "2.1849.an_eiq", 2], ["2.43.t_gs", "2.1849.an_eiq", 2], ["2.43.aq_fl", "2.79507.xk_lqxy", 3], ["2.43.c_acf", "2.79507.xk_lqxy", 3], ["2.43.ay_iv", "2.6321363049.chaa_anqbjroc", 6], ["2.43.ag_bf", "2.6321363049.chaa_anqbjroc", 6], ["2.43.ac_acf", "2.6321363049.chaa_anqbjroc", 6], ["2.43.g_bf", "2.6321363049.chaa_anqbjroc", 6], ["2.43.q_fl", "2.6321363049.chaa_anqbjroc", 6], ["2.43.y_iv", "2.6321363049.chaa_anqbjroc", 6]], "twist_count": 12, "max_twist_degree": 6, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": false, "is_geometrically_simple": false, "simple_distinct": ["1.43.al", "1.43.ai"], "simple_multiplicities": [1, 1], "simple_factors": ["1.43.alA", "1.43.aiA"], "dim1_factors": 2, "dim2_factors": 0, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 2, "dim2_distinct": 0, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 2, "geom_dim2_factors": 0, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 2, "geom_dim2_distinct": 0, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -19, 88], "jacobian_count": 12, "curves": ["y^2=26*x^6+19*x^5+19*x^4+20*x^3+17*x^2+35*x+19", "y^2=7*x^6+x^5+3*x^4+26*x^3+6*x^2+41*x+14", "y^2=7*x^6+14*x^5+12*x^4+4*x^3+26*x^2+40*x+33", "y^2=27*x^6+20*x^5+29*x^4+20*x^3+12*x^2+16*x+27", "y^2=2*x^6+35*x^5+32*x^4+16*x^3+16*x^2+24*x+40", "y^2=17*x^6+13*x^5+22*x^4+39*x^3+18*x^2+5*x+27", "y^2=22*x^6+14*x^5+27*x^4+13*x^3+24*x^2+7*x+39", "y^2=34*x^6+11*x^5+19*x^4+27*x^3+32*x^2+17*x+20", "y^2=30*x^6+10*x^5+24*x^3+8*x^2+41*x+23", "y^2=5*x^6+2*x^5+41*x^4+35*x^3+12*x^2+32*x+29", "y^2=32*x^6+26*x^5+33*x^4+4*x^3+17*x^2+38*x+18", "y^2=3*x^6+8*x^5+5*x^4+22*x^3+36*x^2+6*x+22"], "hyp_count": 12, "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_index": 54, "zfv_index_factorization": [[2, 1], [3, 3]], "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 5508, "geometric_splitting_field": "4.0.2601.1", "splitting_field": "4.0.2601.1", "geometric_splitting_polynomials": [[16, 4, 5, -1, 1]], "splitting_polynomials": [[16, 4, 5, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 56, "principal_polarization_count": 24, "pic_prime_gens": [[1, 5, 1, 6], [2, 7, 1, 3]]}