# Stored data for abelian variety isogeny class 2.59.az_kh, downloaded from the LMFDB on 31 October 2025.
{"abvar_count": 2249, "abvar_counts": [2249, 11805001, 42175161899, 146839161063725, 511100668270704304, 1779177377944402117201, 6193374467026710222997439, 21559173466582676238902520725, 75047496266315174225103850378229, 261240336029697708729857952628124416], "abvar_counts_str": "2249 11805001 42175161899 146839161063725 511100668270704304 1779177377944402117201 6193374467026710222997439 21559173466582676238902520725 75047496266315174225103850378229 261240336029697708729857952628124416 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.0473576671055406, 0.279593066243873], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 35, "curve_counts": [35, 3391, 205355, 12118083, 714901800, 42180058531, 2488646765045, 146830410767283, 8662995785442665, 511116754328017206], "curve_counts_str": "35 3391 205355 12118083 714901800 42180058531 2488646765045 146830410767283 8662995785442665 511116754328017206 ", "curves": ["y^2=50*x^6+10*x^5+38*x^4+43*x^3+14*x^2+44*x+18", "y^2=36*x^6+43*x^5+15*x^4+35*x^3+14*x^2+53*x+18", "y^2=34*x^6+58*x^5+27*x^4+45*x^3+50*x^2+17*x+39", "y^2=47*x^6+6*x^5+32*x^4+11*x^3+39*x^2+26*x+4"], "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": 1, "g": 2, "galois_groups": ["4T1"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T1"], "geometric_number_fields": ["4.0.609725.2"], "geometric_splitting_field": "4.0.609725.2", "geometric_splitting_polynomials": [[139, -107, 33, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 4, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 4, "label": "2.59.az_kh", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.609725.2"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 2], [1, 5, 2, 2]], "poly": [1, -25, 267, -1475, 3481], "poly_str": "1 -25 267 -1475 3481 ", "primitive_models": [], "principal_polarization_count": 4, "q": 59, "real_poly": [1, -25, 149], "simple_distinct": ["2.59.az_kh"], "simple_factors": ["2.59.az_khA"], "simple_multiplicities": [1], "singular_primes": [], "size": 4, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.609725.2", "splitting_polynomials": [[139, -107, 33, -1, 1]], "twist_count": 2, "twists": [["2.59.z_kh", "2.3481.adn_grd", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 4, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 725, "zfv_singular_count": 0, "zfv_singular_primes": []}