# Stored data for abelian variety isogeny class 2.81.abb_mt, downloaded from the LMFDB on 03 November 2025.
{"abvar_count": 4679, "abvar_counts": [4679, 42611653, 282730675871, 1853221738768533, 12157558519443173744, 79766245958542830005053, 523347583278096840455213759, 3433683958361527126079973163077, 22528399756037693056694733707909759, 147808829574025608338568292471545879808], "abvar_counts_str": "4679 42611653 282730675871 1853221738768533 12157558519443173744 79766245958542830005053 523347583278096840455213759 3433683958361527126079973163077 22528399756037693056694733707909759 147808829574025608338568292471545879808 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.0987890015234228, 0.315475092414614], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 55, "curve_counts": [55, 6495, 532009, 43051403, 3486753730, 282428838543, 22876790280301, 1853020263362099, 150094636703435251, 12157665472191003390], "curve_counts_str": "55 6495 532009 43051403 3486753730 282428838543 22876790280301 1853020263362099 150094636703435251 12157665472191003390 ", "curves": ["y^2=(2*a^3+2*a^2)*x^6+(2*a^3+2*a+1)*x^5+(a^2+2)*x^4+(a^3+2*a)*x^3+(a^3+2*a^2)*x^2+(2*a^3+2)*x+a^3+1", "y^2=(a^3+a+2)*x^6+(2*a^2+a+1)*x^5+(a^3+2*a^2+2*a+1)*x^4+(2*a^3+a^2+2*a+1)*x^3+(2*a^3+2*a^2+a+1)*x^2+(2*a^3+a^2)*x+a^3+a^2+a", "y^2=(a^3+a)*x^6+(a^3+2*a^2+2)*x^5+(2*a^3+a+1)*x^4+(2*a^3+a+2)*x^3+a^3*x^2+(2*a^3+2*a)*x+2*a^3+2*a^2+2*a+1", "y^2=(a^2+a+2)*x^6+(2*a^3+2*a+1)*x^5+(2*a^2+2*a+2)*x^4+(a^2+a+2)*x^3+(2*a^3+a^2+1)*x^2+(a^2+1)*x+a^2+2*a", "y^2=(a^3+2*a^2)*x^6+(2*a^2+2*a)*x^5+2*x^4+(2*a^3+2*a^2)*x^3+(2*a^3+2)*x^2+(a^3+2*a^2+a+2)*x+2*a^3+2*a^2+2*a", "y^2=(a+1)*x^6+(a+2)*x^5+2*a^2*x^4+(2*a^3+a^2)*x^3+(a^3+a^2+2)*x^2+(a^3+a^2+2*a+1)*x+2*a^2+a+2", "y^2=(a^3+2*a^2)*x^6+(a^3+2*a^2+2*a)*x^5+(a^3+2*a)*x^4+(a^3+a^2+a+1)*x^3+(2*a^3+2*a^2+2*a+2)*x^2+(a^3+2*a^2)*x+a^3+a^2+2*a", "y^2=(a^3+a^2+2*a+2)*x^6+(2*a^3+2)*x^5+(a^3+a^2+a+2)*x^4+(a^3+a^2+2)*x^3+(a^2+2*a+1)*x^2+(2*a^3+a^2+1)*x+2*a+1", "y^2=2*a^3*x^6+(2*a^3+2*a^2+2*a+2)*x^5+(a^3+1)*x^4+(2*a^3+2*a^2)*x^3+(2*a^2+1)*x^2+(a^3+a)*x+a^3+a^2+2", "y^2=(a+2)*x^6+(2*a^3+a+2)*x^5+(2*a^3+2*a)*x^4+(a^3+2*a^2+a+1)*x^3+(a^3+a^2+2)*x^2+(2*a^2+1)*x+2*a^3+a^2+2*a", "y^2=(2*a^3+a^2+2)*x^6+(2*a^3+2*a^2+2*a+2)*x^5+x^4+(2*a^3+a^2+a+2)*x^3+2*a^2*x^2+(2*a^2+2)*x+a+1", "y^2=(2*a^3+2*a^2+2*a+2)*x^6+(2*a^3+a+2)*x^5+(a^3+2*a^2+2*a+1)*x^4+(2*a^3+2*a+1)*x^3+(a^3+2*a^2+2)*x^2+(2*a^3+a+1)*x+a", "y^2=(a^3+2*a^2+a+1)*x^6+(2*a^3+2*a^2+2*a)*x^5+(a^2+2*a+2)*x^4+(a^3+a+1)*x^3+(a^3+2*a^2+2*a)*x^2+(2*a^3+2*a^2+a+1)*x+2*a+1", "y^2=(2*a^3+a+1)*x^6+(2*a^3+a^2+2*a+2)*x^5+(2*a^2+2*a+2)*x^4+(a^3+2*a^2+a)*x^3+(2*a^3+2*a^2+2*a)*x^2+2*x+2*a^3+a+1", "y^2=(a^2+a)*x^6+2*a*x^5+(a^2+1)*x^4+(2*a^3+2*a^2+a)*x^3+a^3*x^2+(2*a^2+a+1)*x+2*a^3+2*a", "y^2=(a^3+a^2+a+1)*x^6+2*a^2*x^5+2*a*x^4+(2*a^3+a+2)*x^3+(a^3+a^2+a+2)*x^2+(a^3+a+2)*x+a^3+2*a^2+a+2", "y^2=a*x^6+a^2*x^5+(a^3+a+2)*x^4+(2*a^3+2*a^2+a+2)*x^3+(a^2+2*a+1)*x^2+(a^3+a^2+2*a+1)*x+2*a^3+a^2", "y^2=2*a^2*x^6+(a^3+a^2+a)*x^5+2*a*x^4+(a^3+a^2+a+2)*x^3+(2*a^3+2*a+2)*x^2+(2*a^3+2*a^2+2*a+2)*x+2*a^3+a^2+a+2", "y^2=(2*a^3+a^2+2*a+1)*x^6+(a^2+a+1)*x^5+(a^3+2*a^2+2*a+1)*x^4+(2*a^3+2*a)*x^3+(2*a^2+2)*x^2+(2*a^3+a^2+2)*x+a^3+a^2+a", "y^2=(a^3+2*a)*x^6+2*x^5+a^3*x^4+(a^2+a)*x^3+(a^2+2*a+2)*x^2+(a^3+2*a^2+a+1)*x+2*a^3+a^2+a+1", "y^2=(a^2+1)*x^6+(2*a^3+2*a^2+a)*x^5+(a^3+a^2+a+2)*x^4+2*x^3+(2*a^3+2*a^2+2*a+1)*x^2+2*a*x+2*a^3+a^2+2*a+2", "y^2=(2*a^3+a^2+a+1)*x^6+(a^3+a^2+a+2)*x^5+(a^3+a^2+2*a+2)*x^4+(a^3+2*a^2)*x^3+(2*a^2+2*a+2)*x^2+(a^3+1)*x+a^3+2*a^2", "y^2=(2*a^3+a+2)*x^6+(2*a^2+2*a+2)*x^5+(a^3+2)*x^4+(2*a^3+a^2+a+2)*x^3+(a^3+2*a^2+a+1)*x^2+(2*a^3+2*a+1)*x+2*a^2+2*a+2", "y^2=(a^3+a^2+2*a+2)*x^6+(2*a^3+2*a)*x^5+(2*a^2+a)*x^4+2*a*x^3+(2*a^2+a+2)*x^2+(a^3+2*a^2+a+1)*x+a^3+a^2+a+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": 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": ["4.0.19250077.2"], "geometric_splitting_field": "4.0.19250077.2", "geometric_splitting_polynomials": [[611, 150, 58, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 24, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 24, "label": "2.81.abb_mt", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.19250077.2"], "p": 3, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -27, 331, -2187, 6561], "poly_str": "1 -27 331 -2187 6561 ", "primitive_models": [], "q": 81, "real_poly": [1, -27, 169], "simple_distinct": ["2.81.abb_mt"], "simple_factors": ["2.81.abb_mtA"], "simple_multiplicities": [1], "singular_primes": [], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.19250077.2", "splitting_polynomials": [[611, 150, 58, -1, 1]], "twist_count": 2, "twists": [["2.81.bb_mt", "2.6561.acp_guj", 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": 6853, "zfv_singular_count": 0, "zfv_singular_primes": []}