# Stored data for abelian variety isogeny class 2.59.g_ax, downloaded from the LMFDB on 13 December 2025.
{"abvar_count": 3819, "abvar_counts": [3819, 11835081, 42529163076, 146827541611449, 511151418756219099, 1779171691834536371856, 6193383647274866904852099, 21559173856999066979345587689, 75047498013640944562456090703076, 261240335975349536278672846717231401], "abvar_counts_str": "3819 11835081 42529163076 146827541611449 511151418756219099 1779171691834536371856 6193383647274866904852099 21559173856999066979345587689 75047498013640944562456090703076 261240335975349536278672846717231401 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.294387598742271, 0.961054265408938], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 66, "curve_counts": [66, 3400, 207072, 12117124, 714972786, 42179923726, 2488650453894, 146830413426244, 8662995987142608, 511116754221685000], "curve_counts_str": "66 3400 207072 12117124 714972786 42179923726 2488650453894 146830413426244 8662995987142608 511116754221685000 ", "curves": ["y^2=41*x^6+47*x^5+36*x^4+11*x^3+3*x^2+22*x+41", "y^2=4*x^6+40*x^5+13*x^4+43*x^3+50*x^2+43*x+4", "y^2=42*x^6+52*x^5+47*x^4+18*x^3+4*x^2+23*x+42", "y^2=33*x^6+16*x^5+49*x^4+53*x^3+51*x^2+5*x+33", "y^2=2*x^6+28*x^5+53*x^4+29*x^3+46*x^2+19*x+2", "y^2=9*x^6+34*x^5+25*x^4+29*x^3+49*x^2+20*x+9", "y^2=49*x^6+11*x^5+3*x^4+28*x^3+34*x^2+47*x+49"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 4, "g": 2, "galois_groups": ["4T2"], "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.8.1"], "geometric_splitting_field": "2.0.8.1", "geometric_splitting_polynomials": [[2, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 7, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 7, "label": "2.59.g_ax", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 24, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.576.1"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 6, -23, 354, 3481], "poly_str": "1 6 -23 354 3481 ", "primitive_models": [], "q": 59, "real_poly": [1, 6, -141], "simple_distinct": ["2.59.g_ax"], "simple_factors": ["2.59.g_axA"], "simple_multiplicities": [1], "singular_primes": ["5,11*F^2+9*F+V+12", "23,F^2+17*F-5*V-33"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.576.1", "splitting_polynomials": [[4, 0, -2, 0, 1]], "twist_count": 8, "twists": [["2.59.ag_ax", "2.3481.ade_eut", 2], ["2.59.am_fy", "2.205379.cnc_cmcjy", 3], ["2.59.a_de", "2.42180533641.abisgi_wcdpqueo", 6], ["2.59.m_fy", "2.42180533641.abisgi_wcdpqueo", 6], ["2.59.a_ade", "2.1779197418239532716881.acdyclblk_ceigjnmadzwmkwyo", 12], ["2.59.au_hs", "2.3165543453070218706859776348972393302368161.eeaeylrhpthsiahg_gorsymkwftiezorbjwumaotrcfwcedy", 24], ["2.59.u_hs", "2.3165543453070218706859776348972393302368161.eeaeylrhpthsiahg_gorsymkwftiezorbjwumaotrcfwcedy", 24]], "weak_equivalence_count": 4, "zfv_index": 575, "zfv_index_factorization": [[5, 2], [23, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 5, "zfv_plus_index_factorization": [[5, 1]], "zfv_plus_norm": 529, "zfv_singular_count": 4, "zfv_singular_primes": ["5,11*F^2+9*F+V+12", "23,F^2+17*F-5*V-33"]}