# Stored data for abelian variety isogeny class 3.3.ad_j_ap, downloaded from the LMFDB on 01 July 2026.
{"abvar_count": 19, "abvar_counts": [19, 2071, 27037, 598519, 15914989, 374273191, 9957815488, 285882001831, 7657018424623, 202809463408711], "abvar_counts_str": "19 2071 27037 598519 15914989 374273191 9957815488 285882001831 7657018424623 202809463408711 ", "angle_corank": 0, "angle_rank": 3, "angles": [0.239076736162462, 0.372844462505073, 0.581699150201732], "center_dim": 6, "cohen_macaulay_max": 1, "curve_count": 1, "curve_counts": [1, 19, 37, 91, 271, 703, 2080, 6643, 19765, 58159], "curve_counts_str": "1 19 37 91 271 703 2080 6643 19765 58159 ", "curves": ["y^2=2*x^8+2*x^7+x^6+2*x^5+x^4+x^2+x+2"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 1, "dim3_factors": 1, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 2, "g": 3, "galois_groups": ["6T6"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "geom_dim3_distinct": 1, "geom_dim3_factors": 1, "geom_dim4_distinct": 0, "geom_dim4_factors": 0, "geom_dim5_distinct": 0, "geom_dim5_factors": 0, "geometric_center_dim": 6, "geometric_extension_degree": 1, "geometric_galois_groups": ["6T6"], "geometric_number_fields": ["6.0.465831.1"], "geometric_splitting_field": "6.0.465831.1", "geometric_splitting_polynomials": [[3, -9, 15, -13, 9, -3, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 1, "is_cyclic": true, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 1, "label": "3.3.ad_j_ap", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 1, "newton_elevation": 3, "noncyclic_primes": [], "number_fields": ["6.0.465831.1"], "p": 3, "p_rank": 0, "p_rank_deficit": 3, "poly": [1, -3, 9, -15, 27, -27, 27], "poly_str": "1 -3 9 -15 27 -27 27 ", "primitive_models": [], "q": 3, "real_poly": [1, -3, 0, 3], "simple_distinct": ["3.3.ad_j_ap"], "simple_factors": ["3.3.ad_j_apA"], "simple_multiplicities": [1], "singular_primes": ["3,F^3+3*F+V+3,6*F^3-F^2-F+9"], "slopes": ["1/3A", "1/3B", "1/3C", "2/3A", "2/3B", "2/3C"], "splitting_field": "6.0.465831.1", "splitting_polynomials": [[3, -9, 15, -13, 9, -3, 1]], "twist_count": 2, "twists": [["3.3.d_j_p", "3.9.j_bt_fx", 2]], "weak_equivalence_count": 2, "zfv_index": 3, "zfv_index_factorization": [[3, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 639, "zfv_singular_count": 3, "zfv_singular_primes": ["3,F^3+3*F+V+3,6*F^3-F^2-F+9"]}