# Stored data for abelian variety isogeny class 3.5.d_j_v, downloaded from the LMFDB on 06 October 2026.
{"abvar_count": 279, "abvar_counts": [279, 22599, 2101707, 248430807, 29957095179, 3819635996679, 469599929948736, 59969746222317927, 7465530020296348359, 930757275293737603239], "abvar_counts_str": "279 22599 2101707 248430807 29957095179 3819635996679 469599929948736 59969746222317927 7465530020296348359 930757275293737603239 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 3, "angles": [0.348097716608178, 0.579933069652494, 0.843561104768793], "center_dim": 6, "cohen_macaulay_max": 1, "curve_count": 9, "curve_counts": [9, 35, 135, 635, 3069, 15647, 76932, 393011, 1957041, 9759695], "curve_counts_str": "9 35 135 635 3069 15647 76932 393011 1957041 9759695 ", "curves": ["y^2=x^7+x^4+x^2+x+4", "y^2=x^7+2*x^4+x^3+x^2+4*x+4", "y^2=x^7+2*x^4+3*x^3+x^2+2*x+4", "y^2=x^7+3*x^5+2*x^4+2*x^2+2*x+1", "y^2=x^7+3*x^5+2*x^4+3*x^3+x^2+4*x+4", "y^2=x^7+4*x^5+2*x^4+x^3+3*x^2+x+1", "2*x^3*y+4*x^3*z+2*x^2*y^2+x^2*z^2+x*z^3+y^3*z=0", "4*x^3*y+3*x^3*z+4*x^2*y^2+x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "4*x^4+x^3*y+2*x^3*z+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "2*x^4+2*x^3*y+x^3*z+x^2*y^2+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "x^4+2*x^3*z+x^2*y^2+3*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "2*x^4+2*x^3*y+3*x^3*z+x^2*y^2+4*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "2*x^4+4*x^3*y+2*x^3*z+3*x^2*y^2+4*x^2*y*z+x^2*z^2+x*z^3+y^3*z=0", "2*x^4+3*x^3*z+2*x^2*y^2+x*y*z^2+x*z^3+y^3*z=0", "x^3*y+4*x^3*z+4*x^2*y^2+x*y*z^2+x*z^3+y^3*z=0", "3*x^4+4*x^3*y+x^3*z+x^2*y^2+x^2*y*z+x*y*z^2+x*z^3+y^3*z=0", "x^4+4*x^3*y+4*x^3*z+3*x^2*y^2+3*x^2*y*z+x*y*z^2+x*z^3+y^3*z=0", "x^4+x^3*y+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0", "4*x^4+x^3*z+x^2*y^2+x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0", "x^4+x^3*y+4*x^3*z+3*x^2*y^2+x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0", "3*x^4+x^3*y+3*x^3*z+2*x^2*y^2+2*x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0", "x^4+3*x^3*y+2*x^3*z+3*x^2*y^2+3*x^2*y*z+x^2*z^2+x*y*z^2+x*z^3+y^3*z=0", "4*x^4+x^3*y+4*x^3*z+x^2*y^2+x*z^3+y^4+y^2*z^2=0", "x^4+3*x^3*y+x^3*z+x^2*y^2+x^2*y*z+x*z^3+y^4+y^2*z^2=0", "4*x^4+x^3*y+4*x^3*z+2*x^2*y^2+2*x^2*y*z+x*z^3+y^4+y^2*z^2=0", "2*x^4+4*x^3*y+2*x^3*z+3*x^2*y^2+2*x^2*y*z+x*z^3+y^4+y^2*z^2=0", "2*x^4+3*x^3*y+3*x^3*z+x^2*y^2+2*x^2*y*z+x^2*z^2+x*z^3+y^4+y^2*z^2=0", "4*x^4+4*x^3*y+x^3*z+x^2*y^2+2*x^2*y*z+3*x^2*z^2+x*z^3+y^4+y^2*z^2=0", "4*x^4+x^3*y+x^3*z+4*x^2*y^2+2*x^2*y*z+4*x^2*z^2+x*z^3+y^4+y^2*z^2=0", "4*x^4+3*x^3*y+3*x^3*z+x^2*y^2+x^2*y*z+x*y^3+x*z^3+y^4+y^2*z^2=0"], "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": 4, "g": 3, "galois_groups": ["6T11"], "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": ["6T11"], "geometric_number_fields": ["6.0.135911079.1"], "geometric_splitting_field": "6.0.135911079.1", "geometric_splitting_polynomials": [[81, 21, 21, -5, 9, -3, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 6, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 30, "label": "3.5.d_j_v", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 4, "newton_elevation": 0, "noncyclic_primes": [3], "number_fields": ["6.0.135911079.1"], "p": 5, "p_rank": 3, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 13], [1, 31, 1, 26]], "poly": [1, 3, 9, 21, 45, 75, 125], "poly_str": "1 3 9 21 45 75 125 ", "primitive_models": [], "principal_polarization_count": 39, "q": 5, "real_poly": [1, 3, -6, -9], "simple_distinct": ["3.5.d_j_v"], "simple_factors": ["3.5.d_j_vA"], "simple_multiplicities": [1], "singular_primes": ["3,-F^3+3*F^2-4*F-V-4", "3,F^3-3*F^2+5*F+V^2+V+3"], "size": 65, "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "splitting_field": "6.0.135911079.1", "splitting_polynomials": [[81, 21, 21, -5, 9, -3, 1]], "twist_count": 2, "twists": [["3.5.ad_j_av", "3.25.j_bt_gn", 2]], "weak_equivalence_count": 4, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 26, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 1319, "zfv_singular_count": 4, "zfv_singular_primes": ["3,-F^3+3*F^2-4*F-V-4", "3,F^3-3*F^2+5*F+V^2+V+3"]}