# Stored data for abelian variety isogeny class 2.67.af_abq, downloaded from the LMFDB on 08 October 2025.
{"abvar_count": 4108, "abvar_counts": [4108, 19669104, 89930413456, 406126164540096, 1822738608157901668, 8182687629038940815616, 36732249760032624252530452, 164890945812905366017252633344, 740195519980553123533589305703824, 3322737666621695245970068293044343024], "abvar_counts_str": "4108 19669104 89930413456 406126164540096 1822738608157901668 8182687629038940815616 36732249760032624252530452 164890945812905366017252633344 740195519980553123533589305703824 3322737666621695245970068293044343024 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.0678686046651515, 0.734535271331818], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 63, "curve_counts": [63, 4381, 299004, 20154025, 1350051633, 90458036422, 6060715663779, 406067645681809, 27206534621379588, 1822837807250086861], "curve_counts_str": "63 4381 299004 20154025 1350051633 90458036422 6060715663779 406067645681809 27206534621379588 1822837807250086861 ", "curves": ["y^2=25*x^6+60*x^5+32*x^4+44*x^3+36*x^2+43", "y^2=8*x^6+42*x^5+38*x^4+37*x^3+13*x^2+16*x+31", "y^2=22*x^6+26*x^5+40*x^4+31*x^3+41*x^2+33*x+7", "y^2=35*x^6+48*x^5+40*x^4+14*x^3+32*x^2+40*x+18", "y^2=60*x^6+63*x^5+44*x^4+18*x^3+42*x^2+39*x+42", "y^2=47*x^6+41*x^5+34*x^4+48*x^3+57*x^2+x+58", "y^2=58*x^6+2*x^5+42*x^4+10*x^3+53*x^2+33*x+1", "y^2=60*x^6+57*x^5+12*x^4+63*x^3+21*x^2+21*x+7", "y^2=58*x^6+31*x^5+31*x^4+37*x^3+37*x^2+6*x+6", "y^2=36*x^6+7*x^5+20*x^4+42*x^3+54*x^2+24*x+2", "y^2=43*x^6+44*x^5+33*x^4+35*x^3+18*x^2+25*x+64", "y^2=26*x^6+47*x^5+10*x^4+48*x^3+8*x^2+65*x+15", "y^2=16*x^6+3*x^5+63*x^4+65*x^3+7*x^2+10*x", "y^2=5*x^6+13*x^5+49*x^4+46*x^3+52*x^2+60*x+6", "y^2=34*x^6+65*x^5+31*x^4+7*x^3+50*x^2+4*x+55", "y^2=2*x^6+4*x^3+66", "y^2=3*x^6+10*x^5+60*x^4+55*x^3+18*x^2+27*x+45", "y^2=63*x^6+54*x^5+29*x^3+5*x^2+5*x+64", "y^2=56*x^6+16*x^5+31*x^4+6*x^3+15*x^2+15*x+16", "y^2=2*x^6+2*x^3+3", "y^2=47*x^6+20*x^5+33*x^4+54*x^3+64*x^2+22*x+56", "y^2=27*x^6+32*x^5+66*x^4+27*x^3+36*x^2+22*x+19", "y^2=8*x^6+31*x^5+14*x^4+44*x^3+30*x^2+47*x+25", "y^2=63*x^6+14*x^5+32*x^4+15*x^3+20*x^2+62*x+64", "y^2=10*x^6+11*x^5+7*x^4+11*x^3+x^2+31*x+15", "y^2=30*x^6+4*x^5+11*x^4+11*x^3+61*x^2+40*x+14", "y^2=3*x^6+33*x^5+5*x^4+13*x^3+9*x^2+58*x+3", "y^2=36*x^6+46*x^5+8*x^4+8*x^3+7*x^2+65*x+6", "y^2=47*x^6+21*x^5+52*x^4+15*x^3+x^2+2*x+37", "y^2=2*x^6+2*x^3+63", "y^2=2*x^6+2*x^3+38", "y^2=11*x^6+24*x^5+19*x^4+35*x^3+33*x^2+27*x+21", "y^2=38*x^6+23*x^5+58*x^3+33*x^2+36*x+19"], "dim1_distinct": 2, "dim1_factors": 2, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 28, "g": 2, "galois_groups": ["2T1", "2T1"], "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": ["2.0.3.1"], "geometric_splitting_field": "2.0.3.1", "geometric_splitting_polynomials": [[1, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 33, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 33, "label": "2.67.af_abq", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.3.1", "2.0.3.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -5, -42, -335, 4489], "poly_str": "1 -5 -42 -335 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, -5, -176], "simple_distinct": ["1.67.aq", "1.67.l"], "simple_factors": ["1.67.aqA", "1.67.lA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,F-3*V+4", "2,-V-9", "7,18*F-34"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.67.abb_ly", "2.4489.aef_kyi", 2], ["2.67.f_abq", "2.4489.aef_kyi", 2], ["2.67.bb_ly", "2.4489.aef_kyi", 2], ["2.67.abg_pa", "2.300763.acps_dahkg", 3], ["2.67.al_cc", "2.300763.acps_dahkg", 3], ["2.67.k_gd", "2.300763.acps_dahkg", 3], ["2.67.q_hh", "2.300763.acps_dahkg", 3], ["2.67.w_jv", "2.300763.acps_dahkg", 3], ["2.67.aw_jv", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.av_ig", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.aq_hh", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.ak_gd", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.ag_db", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_aes", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_n", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_ef", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.g_db", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.l_cc", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.v_ig", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.bg_pa", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.a_aef", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12], ["2.67.a_an", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12], ["2.67.a_es", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12]], "weak_equivalence_count": 28, "zfv_index": 10206, "zfv_index_factorization": [[2, 1], [3, 6], [7, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1764, "zfv_singular_count": 6, "zfv_singular_primes": ["3,F-3*V+4", "2,-V-9", "7,18*F-34"]}