# Stored data for abelian variety isogeny class 2.31.aw_hb, downloaded from the LMFDB on 11 June 2026.
{"abvar_count": 441, "abvar_counts": [441, 815409, 869306256, 850015773369, 819193181645601, 787600160998560000, 756935545547496412881, 727422126529443458724009, 699053530568242162937669136, 671790527971753837735721993409], "abvar_counts_str": "441 815409 869306256 850015773369 819193181645601 787600160998560000 756935545547496412881 727422126529443458724009 699053530568242162937669136 671790527971753837735721993409 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.049712642025706, 0.049712642025706], "center_dim": 2, "curve_count": 10, "curve_counts": [10, 844, 29176, 920404, 28613950, 887433118, 27512309170, 852889870564, 26439618778216, 819628285947004], "curve_counts_str": "10 844 29176 920404 28613950 887433118 27512309170 852889870564 26439618778216 819628285947004 ", "curves": [], "dim1_distinct": 1, "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, "g": 2, "galois_groups": ["2T1"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": -1, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 0, "label": "2.31.aw_hb", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [3, 7], "number_fields": ["2.0.3.1"], "p": 31, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -22, 183, -682, 961], "poly_str": "1 -22 183 -682 961 ", "primitive_models": [], "q": 31, "real_poly": [1, -22, 121], "simple_distinct": ["1.31.al"], "simple_factors": ["1.31.alA", "1.31.alB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.31.a_ach", "2.961.aeo_hzv", 2], ["2.31.w_hb", "2.961.aeo_hzv", 2], ["2.31.ah_s", "2.29791.axs_iumg", 3], ["2.31.ae_ap", "2.29791.axs_iumg", 3], ["2.31.i_da", "2.29791.axs_iumg", 3], ["2.31.l_dm", "2.29791.axs_iumg", 3], ["2.31.o_eh", "2.29791.axs_iumg", 3], ["2.31.a_ch", "2.923521.aepy_jjjsd", 4], ["2.31.as_fj", "2.887503681.aeaka_juehjny", 6], ["2.31.ap_ec", "2.887503681.aeaka_juehjny", 6], ["2.31.ao_eh", "2.887503681.aeaka_juehjny", 6], ["2.31.al_dm", "2.887503681.aeaka_juehjny", 6], ["2.31.ai_da", "2.887503681.aeaka_juehjny", 6], ["2.31.ad_bi", "2.887503681.aeaka_juehjny", 6], ["2.31.a_n", "2.887503681.aeaka_juehjny", 6], ["2.31.a_bu", "2.887503681.aeaka_juehjny", 6], ["2.31.d_bi", "2.887503681.aeaka_juehjny", 6], ["2.31.e_ap", "2.887503681.aeaka_juehjny", 6], ["2.31.h_s", "2.887503681.aeaka_juehjny", 6], ["2.31.p_ec", "2.887503681.aeaka_juehjny", 6], ["2.31.s_fj", "2.887503681.aeaka_juehjny", 6], ["2.31.a_abu", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12], ["2.31.a_an", "2.787662783788549761.dlgkxbw_tluogrckpisug", 12]]}