# Stored data for abelian variety isogeny class 2.59.ax_jk, downloaded from the LMFDB on 20 September 2025.
{"abvar_count": 2346, "abvar_counts": [2346, 11978676, 42303531816, 146908878199200, 511136305747439046, 1779197598067537642176, 6193386523752436976839446, 21559179817578756955887043200, 75047498786500197972936049759176, 261240336565704251736567752297036916], "abvar_counts_str": "2346 11978676 42303531816 146908878199200 511136305747439046 1779197598067537642176 6193386523752436976839446 21559179817578756955887043200 75047498786500197972936049759176 261240336565704251736567752297036916 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.135062563049179, 0.300760731311381], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 37, "curve_counts": [37, 3441, 205978, 12123833, 714951647, 42180537906, 2488651609733, 146830454021233, 8662996076356462, 511116755376714081], "curve_counts_str": "37 3441 205978 12123833 714951647 42180537906 2488651609733 146830454021233 8662996076356462 511116755376714081 ", "curves": ["y^2=38*x^6+54*x^5+31*x^4+29*x^3+51*x^2+21*x+34", "y^2=21*x^6+13*x^5+24*x^4+15*x^3+11*x^2+20*x+16", "y^2=48*x^6+13*x^4+40*x^3+58*x^2+47*x+2", "y^2=5*x^6+57*x^5+7*x^4+31*x^3+33*x^2+34*x+28", "y^2=20*x^6+56*x^5+41*x^4+16*x^3+33*x^2+54*x+29", "y^2=14*x^6+32*x^5+46*x^4+12*x^3+8*x^2+23*x+30", "y^2=10*x^6+x^5+23*x^4+27*x^3+58*x^2+38*x+29", "y^2=54*x^6+9*x^5+41*x^4+43*x^3+9*x^2+15*x+28", "y^2=56*x^6+30*x^5+17*x^4+15*x^3+16*x^2+7*x+43", "y^2=14*x^6+31*x^5+49*x^4+55*x^3+29*x^2+17*x+20", "y^2=34*x^6+42*x^5+41*x^4+5*x^3+23*x^2+32*x+54", "y^2=10*x^6+14*x^5+31*x^4+52*x^3+39*x^2+39*x+6", "y^2=2*x^6+52*x^5+42*x^4+14*x^2+33*x+10", "y^2=37*x^6+5*x^4+9*x^3+40*x^2+4*x+37", "y^2=47*x^6+26*x^5+6*x^4+17*x^3+40*x^2+56*x+19", "y^2=51*x^6+47*x^5+31*x^4+7*x^3+43*x^2+9*x+56", "y^2=23*x^6+10*x^5+40*x^4+37*x^3+5*x^2+13*x+55", "y^2=44*x^6+43*x^5+53*x^4+26*x^3+21*x^2+11*x+39", "y^2=2*x^6+45*x^5+4*x^4+35*x^3+2*x^2+28*x+22", "y^2=31*x^6+31*x^5+34*x^4+11*x^3+56*x^2+38*x+36"], "dim1_distinct": 2, "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, "endomorphism_ring_count": 3, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.40.1", "2.0.155.1"], "geometric_splitting_field": "4.0.1537600.3", "geometric_splitting_polynomials": [[324, 0, -26, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 20, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 20, "label": "2.59.ax_jk", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.40.1", "2.0.155.1"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 4], [2, 3, 1, 20]], "poly": [1, -23, 244, -1357, 3481], "poly_str": "1 -23 244 -1357 3481 ", "primitive_models": [], "principal_polarization_count": 28, "q": 59, "real_poly": [1, -23, 126], "simple_distinct": ["1.59.ao", "1.59.aj"], "simple_factors": ["1.59.aoA", "1.59.ajA"], "simple_multiplicities": [1, 1], "singular_primes": ["5,-F-8"], "size": 104, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1537600.3", "splitting_polynomials": [[324, 0, -26, 0, 1]], "twist_count": 4, "twists": [["2.59.af_ai", "2.3481.abp_gau", 2], ["2.59.f_ai", "2.3481.abp_gau", 2], ["2.59.x_jk", "2.3481.abp_gau", 2]], "weak_equivalence_count": 3, "zfv_index": 25, "zfv_index_factorization": [[5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 80, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 6200, "zfv_singular_count": 2, "zfv_singular_primes": ["5,-F-8"]}