# Stored data for abelian variety isogeny class 2.53.a_adu, downloaded from the LMFDB on 20 September 2025.
{"abvar_count": 2712, "abvar_counts": [2712, 7354944, 22164245784, 62196819158016, 174887470679011032, 491253791173561774656, 1379946262059303506764248, 3876269036765930093133840384, 10888439761782919953789926264856, 30585627400501943438194061577705024], "abvar_counts_str": "2712 7354944 22164245784 62196819158016 174887470679011032 491253791173561774656 1379946262059303506764248 3876269036765930093133840384 10888439761782919953789926264856 30585627400501943438194061577705024 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0622296275013053, 0.937770372498695], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 54, "curve_counts": [54, 2614, 148878, 7882510, 418195494, 22164130438, 1174711139838, 62259690196894, 3299763591802134, 174887470992509014], "curve_counts_str": "54 2614 148878 7882510 418195494 22164130438 1174711139838 62259690196894 3299763591802134 174887470992509014 ", "curves": ["y^2=13*x^6+43*x^5+35*x^4+37*x^3+50*x^2+52*x+33", "y^2=47*x^6+37*x^5+14*x^4+3*x^3+4*x^2+47*x+12", "y^2=4*x^6+12*x^5+24*x^4+16*x^3+22*x^2+31*x+29", "y^2=22*x^6+24*x^5+7*x^4+x^3+48*x^2+9*x+49", "y^2=42*x^6+18*x^5+38*x^3+39*x^2+16*x+24", "y^2=2*x^6+4*x^5+16*x^4+21*x^3+9*x^2+46*x+24", "y^2=12*x^6+17*x^5+51*x^4+27*x^3+x^2+18*x+23", "y^2=44*x^5+37*x^4+41*x^3+14*x^2+37*x"], "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.408.1"], "geometric_splitting_field": "2.0.408.1", "geometric_splitting_polynomials": [[102, 0, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 8, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 8, "label": "2.53.a_adu", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.665856.2"], "p": 53, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 4], [1, 3, 2, 4], [1, 17, 1, 2]], "poly": [1, 0, -98, 0, 2809], "poly_str": "1 0 -98 0 2809 ", "primitive_models": [], "principal_polarization_count": 14, "q": 53, "real_poly": [1, 0, -204], "simple_distinct": ["2.53.a_adu"], "simple_factors": ["2.53.a_aduA"], "simple_multiplicities": [1], "singular_primes": ["2,-4*F+3*V-1"], "size": 48, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.665856.2", "splitting_polynomials": [[625, 0, 52, 0, 1]], "twist_count": 4, "twists": [["2.53.a_du", "2.7890481.aluq_crhvwo", 4], ["2.53.ae_i", "2.62259690411361.amfgu_wyisliinry", 8], ["2.53.e_i", "2.62259690411361.amfgu_wyisliinry", 8]], "weak_equivalence_count": 5, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 16, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 64, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-4*F+3*V-1"]}