# Stored data for abelian variety isogeny class 2.59.af_abi, downloaded from the LMFDB on 05 September 2025.
{"abvar_count": 3148, "abvar_counts": [3148, 11798704, 41869344400, 146850870322624, 511078667831860228, 1779183343382542240000, 6193391959228264507900468, 21559174266556750249320171264, 75047497061478697136833002163600, 261240336224433817419226029817831984], "abvar_counts_str": "3148 11798704 41869344400 146850870322624 511078667831860228 1779183343382542240000 6193391959228264507900468 21559174266556750249320171264 75047497061478697136833002163600 261240336224433817419226029817831984 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0611433876487223, 0.727810054315389], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 55, "curve_counts": [55, 3389, 203860, 12119049, 714871025, 42180199958, 2488653793835, 146830416215569, 8662995877231180, 511116754709018429], "curve_counts_str": "55 3389 203860 12119049 714871025 42180199958 2488653793835 146830416215569 8662995877231180 511116754709018429 ", "curves": ["y^2=32*x^5+58*x^4+53*x^3+51*x+54", "y^2=58*x^6+47*x^5+25*x^4+43*x^3+48*x^2+13*x+31", "y^2=30*x^6+38*x^5+34*x^4+50*x^3+46*x^2+30*x+44", "y^2=17*x^5+45*x^4+20*x^3+50*x^2+38*x+38", "y^2=44*x^6+57*x^5+56*x^4+34*x^3+50*x^2+39*x+17", "y^2=3*x^6+21*x^5+27*x^4+50*x^3+21*x^2+8*x", "y^2=48*x^6+39*x^5+24*x^4+12*x^3+41*x^2+19*x+47", "y^2=12*x^6+26*x^5+49*x^4+3*x^3+6*x^2+11*x+13", "y^2=44*x^6+37*x^5+32*x^4+16*x^3+26*x^2+52*x+25", "y^2=42*x^6+11*x^5+8*x^4+17*x^3+17*x^2+35*x+20", "y^2=13*x^6+20*x^5+28*x^4+44*x^3+18*x+30", "y^2=38*x^6+19*x^5+14*x^4+58*x^3+3*x^2+13*x+15", "y^2=32*x^6+27*x^5+2*x^4+36*x^3+26*x^2+23*x+2", "y^2=47*x^6+46*x^5+23*x^4+54*x^3+3*x^2+6*x+4", "y^2=23*x^6+56*x^5+26*x^4+3*x^3+4*x^2+18*x+18", "y^2=14*x^6+15*x^5+28*x^4+53*x^3+28*x^2+46*x+52", "y^2=22*x^6+45*x^5+55*x^4+3*x^3+40*x^2+49*x+45", "y^2=x^6+52*x^5+15*x^4+4*x^3+24*x^2+26*x+58", "y^2=27*x^6+56*x^5+40*x^4+6*x^3+12*x^2+37*x+48", "y^2=55*x^6+31*x^5+30*x^4+41*x^3+17*x^2+33*x+29", "y^2=36*x^6+35*x^5+6*x^4+39*x^3+35*x^2+33*x+55"], "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": ["2.0.211.1"], "geometric_splitting_field": "2.0.211.1", "geometric_splitting_polynomials": [[53, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 21, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 21, "label": "2.59.af_abi", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.400689.1"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 13, 1, 9], [1, 13, 2, 9]], "poly": [1, -5, -34, -295, 3481], "poly_str": "1 -5 -34 -295 3481 ", "primitive_models": [], "principal_polarization_count": 21, "q": 59, "real_poly": [1, -5, -152], "simple_distinct": ["2.59.af_abi"], "simple_factors": ["2.59.af_abiA"], "simple_multiplicities": [1], "singular_primes": ["2,-2*F^2-F-3", "17,-F^2-12*F+7*V-35"], "size": 42, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.400689.1", "splitting_polynomials": [[2809, -53, -52, -1, 1]], "twist_count": 6, "twists": [["2.59.f_abi", "2.3481.adp_hqu", 2], ["2.59.k_fn", "2.205379.acgm_cegbu", 3], ["2.59.ak_fn", "2.42180533641.aszqa_nzfdgpfy", 6], ["2.59.a_dp", "2.42180533641.aszqa_nzfdgpfy", 6], ["2.59.f_abi", "2.42180533641.aszqa_nzfdgpfy", 6], ["2.59.a_adp", "2.1779197418239532716881.obywjilw_earxkgpungefmeqg", 12]], "weak_equivalence_count": 4, "zfv_index": 34, "zfv_index_factorization": [[2, 1], [17, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 27, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1156, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-2*F^2-F-3", "17,-F^2-12*F+7*V-35"]}