# Stored data for abelian variety isogeny class 2.81.abe_op, downloaded from the LMFDB on 03 November 2025.
{"abvar_count": 4481, "abvar_counts": [4481, 42125881, 282333399104, 1853095978864809, 12157570794021386801, 79766164027081734071296, 523347315301061296337714801, 3433683598435900758172770717129, 22528399462262267650518070295833664, 147808829433613660216210758339712522201], "abvar_counts_str": "4481 42125881 282333399104 1853095978864809 12157570794021386801 79766164027081734071296 523347315301061296337714801 3433683598435900758172770717129 22528399462262267650518070295833664 147808829433613660216210758339712522201 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.0439844089044582, 0.263626170191107], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 52, "curve_counts": [52, 6420, 531262, 43048484, 3486757252, 282428548446, 22876778566372, 1853020069124804, 150094634746167262, 12157665460641750900], "curve_counts_str": "52 6420 531262 43048484 3486757252 282428548446 22876778566372 1853020069124804 150094634746167262 12157665460641750900 ", "curves": ["y^2=a^2*x^6+(a^3+a^2+2*a+1)*x^5+(a^3+a)*x^4+2*a^2*x^3+(2*a^2+2*a+2)*x^2+(a^3+a^2+a+2)*x+a^3+a+1", "y^2=(a^3+a^2+2*a+1)*x^6+(a+1)*x^5+(a^2+2*a+1)*x^4+2*a^2*x^3+(2*a^3+a^2+2*a)*x^2+(a^3+2*a^2+a+1)*x+2*a^3+a^2+2", "y^2=(2*a^3+a+1)*x^6+(2*a^3+2*a^2+1)*x^5+(2*a^3+2*a+2)*x^4+(a^2+2)*x^3+(2*a^3+1)*x^2+(a^3+2*a^2+a)*x+2*a^3+2*a^2+a+2", "y^2=(2*a^2+1)*x^6+a^3*x^5+(a^3+a^2+a)*x^4+(a^3+a^2)*x^3+(2*a^3+2*a^2+2*a+1)*x^2+(2*a^3+2*a+1)*x+2*a^3+a^2+a+1", "y^2=a^3*x^6+(a^3+1)*x^5+(2*a^3+2)*x^4+(2*a^3+2*a)*x^3+(2*a^3+2*a+1)*x^2+(a^3+2*a^2)*x+2*a^3", "y^2=(a^3+2*a+2)*x^6+(2*a^3+2*a+1)*x^5+(2*a^3+2*a^2+2*a)*x^4+(2*a^3+a^2+2*a)*x^3+(2*a^3+a^2+2*a+1)*x^2+(2*a^2+2*a)*x+a^3+2*a^2+2", "y^2=(2*a^3+2*a^2+2*a+1)*x^6+(2*a^2+1)*x^5+2*a^3*x^4+(2*a^3+1)*x^3+(a^3+a^2+1)*x^2+(2*a^3+2*a^2+2)*x+a^3+a^2+2*a", "y^2=(2*a^2+1)*x^6+(a^3+a^2+2)*x^5+(a^3+a^2)*x^4+(2*a^3+a^2)*x^3+(a^3+1)*x^2+(a^3+a^2+2*a)*x+2*a^3+a", "y^2=(2*a^3+a^2+1)*x^6+(a^3+a^2+1)*x^5+(2*a^3+2*a^2)*x^4+(a^3+a^2+a)*x^3+(a^3+a^2+2*a+2)*x^2+2*x+a^2", "y^2=(a^3+2*a^2+2*a)*x^6+(a^3+a^2+2*a)*x^5+(a^3+a+1)*x^4+(a^3+2*a^2+2)*x^3+(2*a^3+2*a^2+a+2)*x^2+(a^3+a^2+a)*x+a^3+2*a^2+a+2", "y^2=(2*a^2+2*a)*x^6+(2*a^2+a+2)*x^5+(a^2+1)*x^4+(2*a^3+a)*x^3+(a^3+a^2+2*a+1)*x^2+(a^3+2*a^2+1)*x+2*a^3+2*a", "y^2=(a^3+a+2)*x^6+(a^3+a+1)*x^5+(a^3+a^2+2*a+1)*x^4+(2*a^3+a^2+2*a)*x^2+(2*a^3+a^2+2*a)*x+a^3+1"], "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": ["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": ["4.0.69184.1"], "geometric_splitting_field": "4.0.69184.1", "geometric_splitting_polynomials": [[79, -14, 17, -2, 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.abe_op", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.69184.1"], "p": 3, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -30, 379, -2430, 6561], "poly_str": "1 -30 379 -2430 6561 ", "primitive_models": [], "q": 81, "real_poly": [1, -30, 217], "simple_distinct": ["2.81.abe_op"], "simple_factors": ["2.81.abe_opA"], "simple_multiplicities": [1], "singular_primes": ["2,5*F+V-27"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.69184.1", "splitting_polynomials": [[79, -14, 17, -2, 1]], "twist_count": 2, "twists": [["2.81.be_op", "2.6561.afm_qfr", 2]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 1081, "zfv_singular_count": 2, "zfv_singular_primes": ["2,5*F+V-27"]}