# Stored data for abelian variety isogeny class 2.81.abd_ny, downloaded from the LMFDB on 08 November 2025.
{"abvar_count": 4546, "abvar_counts": [4546, 42286892, 282459800200, 1853113095980800, 12157515710003257106, 79766125852891924985600, 523347350858005750641704786, 3433683697717156530003068083200, 22528399573470900792358054980545800, 147808829509839558975231622091913144812], "abvar_counts_str": "4546 42286892 282459800200 1853113095980800 12157515710003257106 79766125852891924985600 523347350858005750641704786 3433683697717156530003068083200 22528399573470900792358054980545800 147808829509839558975231622091913144812 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.0580440523198253, 0.284000150426998], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 53, "curve_counts": [53, 6445, 531500, 43048881, 3486741453, 282428413282, 22876780120653, 1853020122702881, 150094635487090700, 12157665466911531805], "curve_counts_str": "53 6445 531500 43048881 3486741453 282428413282 22876780120653 1853020122702881 150094635487090700 12157665466911531805 ", "curves": ["y^2=(a^3+1)*x^6+(2*a^2+a)*x^5+(2*a^3+a^2+a+2)*x^4+a^3*x^3+(a^3+2*a^2)*x+2*a+2", "y^2=(a+2)*x^6+a*x^5+(a+1)*x^4+(2*a^3+2*a+1)*x^3+2*a^2*x^2+(2*a^2+1)*x+a^3+2*a^2+2*a", "y^2=(2*a^3+a^2+2*a+1)*x^6+(a^2+2*a)*x^5+(a^3+a^2+2)*x^4+a^3*x^3+(2*a^3+a+1)*x^2+a^2*x+2*a^2+2*a", "y^2=(2*a^3+a^2+2*a)*x^6+(2*a^3+a+2)*x^5+(2*a^3+a^2+1)*x^4+(2*a^3+a^2+2*a)*x^3+(2*a^2+2*a+1)*x^2+(a^2+2*a+2)*x+a^3+2*a^2+a+1", "y^2=(2*a^2+2*a)*x^6+(2*a^3+2*a^2+a+1)*x^5+(a^3+a^2+2*a+2)*x^4+(a^3+a)*x^3+(a^2+2*a+1)*x^2+(a^3+2*a^2+2)*x+2*a^3+2*a", "y^2=(a^3+2*a^2+2*a+1)*x^6+(2*a^3+2*a^2+2)*x^5+(a^3+a+2)*x^4+(a^3+2*a^2+2*a)*x^3+(a^3+a+1)*x^2+(a^3+a+2)*x+2*a^2+1", "y^2=(a^2+a)*x^6+(a^2+2*a+2)*x^5+(a^2+a)*x^4+(a^2+2*a)*x^3+(a^3+a^2+a)*x^2+(a^3+a)*x+a^3+2*a+2", "y^2=(2*a^3+2*a^2+2*a)*x^6+(a^3+a^2+2)*x^5+(2*a^3+a^2+a)*x^4+(a^2+2*a+1)*x^3+2*x^2+(2*a^2+1)*x+2*a^2+a+1", "y^2=2*a*x^6+(a^3+2*a^2+a+2)*x^5+(a^3+a^2+a)*x^4+(2*a^3+a+2)*x^3+(2*a^3+a^2)*x^2+(2*a^3+1)*x+a^3+2*a^2+a", "y^2=(2*a^2+1)*x^6+(a^2+a+1)*x^5+(2*a^3+a^2+2*a+2)*x^4+(2*a+1)*x^3+(a^3+2*a+1)*x^2+2*a*x+2*a^3+1", "y^2=(a^3+2*a^2+2*a)*x^6+(2*a^3+a^2+a+1)*x^5+(2*a^2+2*a)*x^4+a^3*x^3+(2*a^3+a^2+2*a+2)*x^2+(a^3+2*a^2)*x+2*a^2+a+1", "y^2=(a^3+2*a^2+a+1)*x^6+(2*a^3+a^2+2)*x^5+(2*a^3+2*a^2+a)*x^4+(a^3+2*a^2+2)*x^3+a^2*x^2+(a^3+a^2)*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": 1, "g": 2, "galois_groups": ["4T3"], "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": ["4T3"], "geometric_number_fields": ["4.0.3516652.1"], "geometric_splitting_field": "4.0.3516652.1", "geometric_splitting_polynomials": [[310, -172, 47, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.81.abd_ny", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.3516652.1"], "p": 3, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -29, 362, -2349, 6561], "poly_str": "1 -29 362 -2349 6561 ", "primitive_models": [], "q": 81, "real_poly": [1, -29, 200], "simple_distinct": ["2.81.abd_ny"], "simple_factors": ["2.81.abd_nyA"], "simple_multiplicities": [1], "singular_primes": [], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.3516652.1", "splitting_polynomials": [[310, -172, 47, -1, 1]], "twist_count": 2, "twists": [["2.81.bd_ny", "2.6561.aen_lsu", 2]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 2092, "zfv_singular_count": 0, "zfv_singular_primes": []}