# Stored data for abelian variety isogeny class 2.64.abb_lv, downloaded from the LMFDB on 03 November 2025.
{"abvar_count": 2649, "abvar_counts": [2649, 16315191, 68719584492, 281559424997691, 1152972791571810999, 4722381292753126898064, 19342812465359708165783589, 79228160199598844333193068979, 324518553658426705819712766907092, 1329227997384074407249099923104502951], "abvar_counts_str": "2649 16315191 68719584492 281559424997691 1152972791571810999 4722381292753126898064 19342812465359708165783589 79228160199598844333193068979 324518553658426705819712766907092 1329227997384074407249099923104502951 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0943151045542547, 0.239018228779079], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 38, "curve_counts": [38, 3982, 262145, 16782250, 1073789588, 68719692247, 4398046363658, 281474968487314, 18014398509481985, 1152921505993895902], "curve_counts_str": "38 3982 262145 16782250 1073789588 68719692247 4398046363658 281474968487314 18014398509481985 1152921505993895902 ", "curves": ["y^2+(x^3+(a^4+a^2)*x+a^4+a^2)*y=(a^5+a^4+a^3+a+1)*x^6+(a^5+1)*x^5+(a^5+1)*x^4+(a^5+1)*x^3+(a^4+a^3+a^2+a+1)*x^2+(a^4+a^3+a+1)*x+a^4+a+1", "y^2+(x^3+a^2*x+a^2)*y=(a^3+a^2+a)*x^6+(a^5+a^4+a^3)*x^5+(a^5+a^4+a^3)*x^4+(a^5+a^4+a^3)*x^3+(a^3+a^2+1)*x^2+(a^5+a^4+a^2)*x+a^5+a^4+a^2", "y^2+(x^3+(a^5+a^2)*x+a^5+a^2)*y=(a^5+a^4+a^2)*x^5+(a^5+a^4+a^2)*x^4+(a^5+a^2+a+1)*x^3+(a^4+a^3+a^2+a+1)*x+a^4", "y^2+(x^3+(a^5+1)*x+a^5+1)*y=(a^4+a^2+a)*x^5+(a^4+a^2+a)*x^4+(a^5+a^2)*x^3+(a^5+a^4+a^3+1)*x+a^5+a^4+a^2+a+1", "y^2+(x^3+(a^4+a+1)*x+a^4+a+1)*y=(a^4+a^2+1)*x^5+(a^4+a^2+1)*x^4+(a^3+a+1)*x^3+(a^5+a^3+a^2+1)*x+a^5+a^3+a^2+a", "y^2+(x^3+(a^5+a^4)*x+a^5+a^4)*y=(a^5+a+1)*x^5+(a^5+a+1)*x^4+(a^5+1)*x^3+(a^4+a^3+a^2)*x+a^4+a+1", "y^2+(x^3+(a^5+a^4+a)*x+a^5+a^4+a)*y=(a^5+a^2+a)*x^5+(a^5+a^2+a)*x^4+(a^4+a^3+a^2+a)*x^3+(a^5+a^4+a^3+a+1)*x+a^5+a^4+a^3+a^2+a", "y^2+(x^3+(a^2+a)*x+a^2+a)*y=(a^5+a^4+a^2)*x^5+(a^5+a^4+a^2)*x^4+(a^5+a^4)*x^3+(a^5+a^4+a^3+a^2)*x+a^5+a^4+a", "y^2+(x^3+a*x+a)*y=(a^5+a^2+1)*x^5+(a^5+a^2+1)*x^4+(a^5+a^4+a^3)*x^3+(a^4+a^3)*x+a^3+1", "y^2+(x^3+(a^5+a^2+a+1)*x+a^5+a^2+a+1)*y=(a^5+a+1)*x^5+(a^5+a+1)*x^4+(a^4+a^2)*x^3+(a^3+a)*x+a^2", "y^2+(x^3+(a^5+a^4+a^2+a+1)*x+a^5+a^4+a^2+a+1)*y=(a^2+a+1)*x^5+(a^2+a+1)*x^4+(a^3+a^2)*x^3+(a^4+a^3+1)*x+a^5+a^3+a", "y^2+(x^3+(a^4+a^2)*x+a^4+a^2)*y=(a^4+a^2+a)*x^5+(a^4+a^2+a)*x^4+(a^2+a)*x^3+(a^3+a^2+1)*x+a", "y^2+(x^3+a^4*x+a^4)*y=(a^5+a^4+1)*x^5+(a^5+a^4+1)*x^4+(a^5+a^4+a^3+a^2+1)*x^3+(a^5+a^4+a^3+a)*x+a^5+a^3", "y^2+(x^3+a^2*x+a^2)*y=a^5*x^5+a^5*x^4+(a^4+a^3+a^2+1)*x^3+(a^5+a^3+a^2)*x+a^4+a^3+a"], "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": 2, "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": 6, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.39.1"], "geometric_splitting_field": "2.0.39.1", "geometric_splitting_polynomials": [[10, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 14, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 14, "label": "2.64.abb_lv", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.1521.1"], "p": 2, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -27, 307, -1728, 4096], "poly_str": "1 -27 307 -1728 4096 ", "primitive_models": [], "q": 64, "real_poly": [1, -27, 179], "simple_distinct": ["2.64.abb_lv"], "simple_factors": ["2.64.abb_lvA"], "simple_multiplicities": [1], "singular_primes": ["17,75*F+18*V-480"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1521.1", "splitting_polynomials": [[9, 3, 4, -1, 1]], "twist_count": 4, "twists": [["2.64.bb_lv", "2.4096.ael_nnd", 2], ["2.64.a_el", "2.262144.a_gdkl", 3], ["2.64.bb_lv", "2.262144.a_gdkl", 3], ["2.64.a_ael", "2.4722366482869645213696.bfiqrrxkw_pbvtotmemtedsgpt", 12]], "weak_equivalence_count": 2, "zfv_index": 17, "zfv_index_factorization": [[17, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2601, "zfv_singular_count": 2, "zfv_singular_primes": ["17,75*F+18*V-480"]}