# Stored data for abelian variety isogeny class 2.89.j_ai, downloaded from the LMFDB on 19 March 2026.
{"abvar_count": 8724, "abvar_counts": [8724, 61975296, 499345742736, 3936185163500544, 31182228579070571124, 246989019636321317093376, 1956411182325194324202996084, 15496731094107911979258387247104, 122749610425121547646457959713319056, 972299657701330293519623853126235742976], "abvar_counts_str": "8724 61975296 499345742736 3936185163500544 31182228579070571124 246989019636321317093376 1956411182325194324202996084 15496731094107911979258387247104 122749610425121547646457959713319056 972299657701330293519623853126235742976 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.324942153926663, 0.991608820593329], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 99, "curve_counts": [99, 7825, 708318, 62735809, 5584150539, 496978506286, 44231339319651, 3936588721601089, 350356406008796622, 31181719927095270625], "curve_counts_str": "99 7825 708318 62735809 5584150539 496978506286 44231339319651 3936588721601089 350356406008796622 31181719927095270625 ", "curves": ["y^2=26*x^6+85*x^5+41*x^4+71*x^3+43*x^2+65*x+65", "y^2=13*x^6+87*x^5+5*x^4+16*x^3+16*x^2+16*x+17", "y^2=75*x^6+63*x^5+69*x^4+65*x^3+30*x^2+66*x+29", "y^2=12*x^6+88*x^5+10*x^4+61*x^3+88*x^2+84*x+54", "y^2=47*x^6+44*x^5+59*x^4+12*x^3+10*x^2+60*x+47", "y^2=41*x^6+39*x^5+52*x^4+80*x^3+56*x+84", "y^2=22*x^6+81*x^5+25*x^4+37*x^3+61*x^2+85*x+11", "y^2=83*x^6+27*x^5+28*x^4+39*x^3+70*x^2+26*x+83", "y^2=53*x^6+22*x^5+65*x^4+16*x^3+38*x^2+29*x+53", "y^2=60*x^6+68*x^5+37*x^4+54*x^3+x^2+57*x+71", "y^2=87*x^6+80*x^5+17*x^4+69*x^3+33*x^2+5*x+84", "y^2=42*x^6+22*x^5+53*x^4+77*x^3+39*x^2+36*x+55", "y^2=81*x^6+53*x^5+61*x^4+44*x^3+32*x^2+77*x+81", "y^2=73*x^6+22*x^5+59*x^4+26*x^3+65*x^2+60*x+73", "y^2=21*x^6+73*x^5+61*x^4+4*x^3+5*x^2+6*x+10"], "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": 8, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 2, "geom_dim2_distinct": 0, "geom_dim2_factors": 0, "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": 2, "geometric_extension_degree": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.11.1"], "geometric_splitting_field": "2.0.11.1", "geometric_splitting_polynomials": [[3, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 15, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 15, "label": "2.89.j_ai", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.1089.1"], "p": 89, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 9, -8, 801, 7921], "poly_str": "1 9 -8 801 7921 ", "primitive_models": [], "q": 89, "real_poly": [1, 9, -186], "simple_distinct": ["2.89.j_ai"], "simple_factors": ["2.89.j_aiA"], "simple_multiplicities": [1], "singular_primes": ["2,-F+4*V+37", "5,-4*F-19*V-168"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1089.1", "splitting_polynomials": [[9, -3, -2, -1, 1]], "twist_count": 6, "twists": [["2.89.aj_ai", "2.7921.adt_cfg", 2], ["2.89.as_jz", "2.704969.eyu_jfrcg", 3], ["2.89.a_dt", "2.496981290961.agcliy_obdcodtxm", 6], ["2.89.s_jz", "2.496981290961.agcliy_obdcodtxm", 6], ["2.89.a_adt", "2.246990403565262140303521.ajbfwibvvg_bfuoektgflhcmvzxry", 12]], "weak_equivalence_count": 8, "zfv_index": 200, "zfv_index_factorization": [[2, 3], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 5, "zfv_plus_index_factorization": [[5, 1]], "zfv_plus_norm": 64, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-F+4*V+37", "5,-4*F-19*V-168"]}