# Stored data for abelian variety isogeny class 3.8.ai_bk_aeq, downloaded from the LMFDB on 14 November 2024.
{"abvar_count": 197, "abvar_counts": [197, 290969, 131937401, 66073531489, 34877605586657, 17957217657134273, 9201447577667415169, 4720493659280892028417, 2418423552371903616547841, 1238019143024621312456854529], "abvar_counts_str": "197 290969 131937401 66073531489 34877605586657 17957217657134273 9201447577667415169 4720493659280892028417 2418423552371903616547841 1238019143024621312456854529 ", "angle_corank": 2, "angle_rank": 1, "angles": [0.0435981566527365, 0.329312442367022, 0.527830414775835], "center_dim": 6, "curve_count": 1, "curve_counts": [1, 73, 505, 3937, 32481, 261313, 2092161, 16770561, 134249473, 1073810433], "curve_counts_str": "1 73 505 3937 32481 261313 2092161 16770561 134249473 1073810433 ", "curves": ["y^2+a*x^4*y=x^8+(a+1)*x", "y^2+a*x^4*y=x^8+(a^2+1)*x", "y^2+a*x^4*y=x^8+(a^2+a)*x"], "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": ["6T1"], "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": 2, "geometric_extension_degree": 7, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.7.1"], "geometric_splitting_field": "2.0.7.1", "geometric_splitting_polynomials": [[2, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 3, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "label": "3.8.ai_bk_aeq", "max_divalg_dim": 1, "max_geom_divalg_dim": 9, "max_twist_degree": 14, "newton_coelevation": 1, "newton_elevation": 3, "number_fields": ["6.0.16807.1"], "p": 2, "p_rank": 0, "p_rank_deficit": 3, "poly": [1, -8, 36, -120, 288, -512, 512], "poly_str": "1 -8 36 -120 288 -512 512 ", "primitive_models": [], "q": 8, "real_poly": [1, -8, 12, 8], "simple_distinct": ["3.8.ai_bk_aeq"], "simple_factors": ["3.8.ai_bk_aeqA"], "simple_multiplicities": [1], "slopes": ["1/3A", "1/3B", "1/3C", "2/3A", "2/3B", "2/3C"], "splitting_field": "6.0.16807.1", "splitting_polynomials": [[1, -1, 1, -1, 1, -1, 1]], "twist_count": 6, "twists": [["3.8.i_bk_eq", "3.64.i_abw_abga", 2], ["3.8.g_i_ai", "3.2097152.ahka_bfyoxc_adesazpwa", 7], ["3.8.g_bk_ea", "3.2097152.ahka_bfyoxc_adesazpwa", 7], ["3.8.ag_i_i", "3.4398046511104.jjhue_dojqpnvzoy_qineghmjvwioke", 14], ["3.8.ag_bk_aea", "3.4398046511104.jjhue_dojqpnvzoy_qineghmjvwioke", 14], ["3.8.i_bk_eq", "3.4398046511104.jjhue_dojqpnvzoy_qineghmjvwioke", 14]]}