# Stored data for abelian variety isogeny class 2.67.a_n, downloaded from the LMFDB on 26 September 2025.
{"abvar_count": 4503, "abvar_counts": [4503, 20277009, 90458209296, 406422817924761, 1822837805812643943, 8182687629038940815616, 36732225162889272212945247, 164890928466652063385649722409, 740195513856780097964376019340304, 3322737666299854228269720408094587249], "abvar_counts_str": "4503 20277009 90458209296 406422817924761 1822837805812643943 8182687629038940815616 36732225162889272212945247 164890928466652063385649722409 740195513856780097964376019340304 3322737666299854228269720408094587249 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.265464728668182, 0.734535271331818], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 68, "curve_counts": [68, 4516, 300764, 20168740, 1350125108, 90458036422, 6060711605324, 406067602964164, 27206534396294948, 1822837807073526436], "curve_counts_str": "68 4516 300764 20168740 1350125108 90458036422 6060711605324 406067602964164 27206534396294948 1822837807073526436 ", "curves": ["y^2=57*x^6+49*x^4+7*x^3+60*x+44", "y^2=47*x^6+31*x^4+14*x^3+53*x+21", "y^2=60*x^6+11*x^5+46*x^4+44*x^3+62*x^2+34*x+59", "y^2=53*x^6+22*x^5+25*x^4+21*x^3+57*x^2+x+51", "y^2=60*x^6+53*x^5+14*x^4+63*x^3+43*x^2+45*x+38", "y^2=57*x^6+45*x^5+14*x^4+39*x^3+32*x^2+30*x+39", "y^2=x^6+48*x^3+42", "y^2=66*x^6+6*x^5+53*x^4+55*x^3+45*x^2+6*x+1", "y^2=65*x^6+12*x^5+39*x^4+43*x^3+23*x^2+12*x+2", "y^2=30*x^6+7*x^5+8*x^4+45*x^3+7*x^2+46*x+49", "y^2=60*x^6+14*x^5+16*x^4+23*x^3+14*x^2+25*x+31", "y^2=54*x^6+29*x^5+45*x^4+34*x^3+36*x^2+40*x+18", "y^2=49*x^6+41*x^5+29*x^4+x^3+12*x^2+13*x+10", "y^2=31*x^6+15*x^5+58*x^4+2*x^3+24*x^2+26*x+20", "y^2=22*x^6+10*x^5+21*x^4+56*x^3+19*x^2+36*x+5", "y^2=44*x^6+20*x^5+42*x^4+45*x^3+38*x^2+5*x+10", "y^2=13*x^6+22*x^5+35*x^4+6*x^3+24*x^2+62*x+11", "y^2=26*x^6+44*x^5+3*x^4+12*x^3+48*x^2+57*x+22", "y^2=54*x^6+21*x^5+52*x^4+14*x^3+9*x^2+43*x+19", "y^2=41*x^6+42*x^5+37*x^4+28*x^3+18*x^2+19*x+38", "y^2=12*x^6+52*x^5+19*x^4+61*x^3+21*x^2+42*x+59", "y^2=24*x^6+37*x^5+38*x^4+55*x^3+42*x^2+17*x+51", "y^2=43*x^6+58*x^5+10*x^4+41*x^3+11*x^2+45*x+10", "y^2=19*x^6+49*x^5+20*x^4+15*x^3+22*x^2+23*x+20", "y^2=15*x^6+3*x^5+29*x^4+54*x^3+62*x^2+31*x+1", "y^2=30*x^6+6*x^5+58*x^4+41*x^3+57*x^2+62*x+2", "y^2=35*x^6+65*x^5+9*x^4+46*x^3+7*x^2+24*x+23", "y^2=3*x^6+63*x^5+18*x^4+25*x^3+14*x^2+48*x+46", "y^2=39*x^6+3*x^5+19*x^4+41*x^3+65*x^2+56*x+61", "y^2=11*x^6+6*x^5+38*x^4+15*x^3+63*x^2+45*x+55", "y^2=36*x^6+21*x^5+37*x^4+11*x^3+35*x^2+23*x+21", "y^2=5*x^6+42*x^5+7*x^4+22*x^3+3*x^2+46*x+42", "y^2=30*x^6+24*x^5+19*x^4+49*x^3+22*x^2+19*x+61", "y^2=60*x^6+48*x^5+38*x^4+31*x^3+44*x^2+38*x+55", "y^2=26*x^6+7*x^5+66*x^4+5*x^3+56*x^2+57*x+24", "y^2=52*x^6+14*x^5+65*x^4+10*x^3+45*x^2+47*x+48", "y^2=5*x^6+16*x^5+35*x^4+44*x^3+56*x^2+66*x+28", "y^2=10*x^6+32*x^5+3*x^4+21*x^3+45*x^2+65*x+56", "y^2=66*x^6+x^5+34*x^4+26*x^3+49*x^2+60*x+48", "y^2=65*x^6+2*x^5+x^4+52*x^3+31*x^2+53*x+29", "y^2=9*x^6+62*x^5+38*x^4+40*x^3+44*x^2+10*x+33", "y^2=18*x^6+57*x^5+9*x^4+13*x^3+21*x^2+20*x+66", "y^2=6*x^6+36*x^5+20*x^4+31*x^3+18*x^2+45*x+35", "y^2=12*x^6+5*x^5+40*x^4+62*x^3+36*x^2+23*x+3", "y^2=35*x^6+42*x^5+36*x^4+39*x^3+34*x^2+24*x+52", "y^2=3*x^6+17*x^5+5*x^4+11*x^3+x^2+48*x+37", "y^2=48*x^6+3*x^5+63*x^4+14*x^3+15*x^2+40*x+55", "y^2=29*x^6+6*x^5+59*x^4+28*x^3+30*x^2+13*x+43", "y^2=44*x^6+22*x^5+47*x^4+35*x^3+60*x^2+53*x+35", "y^2=21*x^6+44*x^5+27*x^4+3*x^3+53*x^2+39*x+3", "y^2=30*x^6+63*x^5+56*x^4+47*x^3+60*x^2+49*x+23", "y^2=60*x^6+59*x^5+45*x^4+27*x^3+53*x^2+31*x+46", "y^2=28*x^6+37*x^5+9*x^3+11*x^2+6*x+32", "y^2=56*x^6+7*x^5+18*x^3+22*x^2+12*x+64", "y^2=63*x^6+47*x^5+66*x^4+62*x^3+7*x^2+50*x+56", "y^2=59*x^6+27*x^5+65*x^4+57*x^3+14*x^2+33*x+45", "y^2=37*x^6+62*x^5+38*x^4+24*x^3+15*x^2+4*x+13", "y^2=19*x^6+55*x^5+29*x^4+45*x^3+26*x^2+47*x+26", "y^2=38*x^6+43*x^5+58*x^4+23*x^3+52*x^2+27*x+52", "y^2=36*x^6+50*x^5+51*x^4+63*x^3+3*x^2+63*x+26", "y^2=5*x^6+33*x^5+35*x^4+59*x^3+6*x^2+59*x+52", "y^2=17*x^6+36*x^5+17*x^4+31*x^3+18*x^2+61*x+26", "y^2=34*x^6+5*x^5+34*x^4+62*x^3+36*x^2+55*x+52", "y^2=25*x^6+54*x^5+66*x^4+54*x^3+9*x^2+22*x+25", "y^2=50*x^6+41*x^5+65*x^4+41*x^3+18*x^2+44*x+50", "y^2=10*x^6+16*x^5+41*x^4+45*x^3+61*x^2+9*x+2", "y^2=20*x^6+32*x^5+15*x^4+23*x^3+55*x^2+18*x+4", "y^2=24*x^6+42*x^5+65*x^4+15*x^3+54*x^2+46*x+29", "y^2=48*x^6+17*x^5+63*x^4+30*x^3+41*x^2+25*x+58", "y^2=55*x^6+64*x^5+18*x^4+25*x^3+48*x^2+x+33", "y^2=43*x^6+61*x^5+36*x^4+50*x^3+29*x^2+2*x+66", "y^2=26*x^6+24*x^5+10*x^4+19*x^3+28*x^2+29*x+27", "y^2=52*x^6+48*x^5+20*x^4+38*x^3+56*x^2+58*x+54", "y^2=8*x^6+44*x^5+33*x^4+9*x^2+13*x+39", "y^2=16*x^6+21*x^5+66*x^4+18*x^2+26*x+11", "y^2=2*x^6+33*x^5+50*x^4+66*x^3+54*x^2+55*x+17", "y^2=49*x^6+55*x^5+54*x^4+24*x^3+36*x^2+63*x+50", "y^2=31*x^6+43*x^5+41*x^4+48*x^3+5*x^2+59*x+33", "y^2=22*x^6+36*x^5+48*x^4+8*x^3+31*x^2+6*x+52", "y^2=44*x^6+5*x^5+29*x^4+16*x^3+62*x^2+12*x+37", "y^2=33*x^6+41*x^5+7*x^3+66*x^2+26*x+44", "y^2=66*x^6+15*x^5+14*x^3+65*x^2+52*x+21", "y^2=20*x^6+9*x^5+66*x^4+65*x^3+6*x^2+56*x+35", "y^2=32*x^6+6*x^5+45*x^4+37*x^3+28*x^2+11*x+20", "y^2=64*x^6+12*x^5+23*x^4+7*x^3+56*x^2+22*x+40", "y^2=27*x^6+48*x^5+41*x^4+21*x^3+54*x^2+30*x+36", "y^2=54*x^6+29*x^5+15*x^4+42*x^3+41*x^2+60*x+5", "y^2=56*x^6+29*x^5+23*x^4+43*x^3+53*x^2+5*x+47", "y^2=45*x^6+58*x^5+46*x^4+19*x^3+39*x^2+10*x+27", "y^2=2*x^6+47*x^5+29*x^4+3*x^3+11*x^2+36*x+49", "y^2=49*x^6+27*x^5+56*x^4+59*x^3+39*x^2+54*x+7", "y^2=31*x^6+54*x^5+45*x^4+51*x^3+11*x^2+41*x+14", "y^2=42*x^6+24*x^5+62*x^4+55*x^3+56*x^2+17*x+42", "y^2=17*x^6+48*x^5+57*x^4+43*x^3+45*x^2+34*x+17", "y^2=32*x^6+9*x^5+62*x^4+5*x^3+4*x^2+11*x+7", "y^2=64*x^6+18*x^5+57*x^4+10*x^3+8*x^2+22*x+14", "y^2=14*x^6+5*x^5+59*x^4+32*x^3+x^2+41*x+26", "y^2=28*x^6+10*x^5+51*x^4+64*x^3+2*x^2+15*x+52", "y^2=x^6+20*x^3+27", "y^2=62*x^6+37*x^5+32*x^4+12*x^3+12*x^2+58*x+45", "y^2=57*x^6+7*x^5+64*x^4+24*x^3+24*x^2+49*x+23", "y^2=10*x^6+59*x^5+63*x^4+60*x^3+64*x^2+66*x+25", "y^2=20*x^6+51*x^5+59*x^4+53*x^3+61*x^2+65*x+50", "y^2=7*x^6+62*x^5+44*x^4+3*x^3+5*x^2+26*x+41", "y^2=14*x^6+57*x^5+21*x^4+6*x^3+10*x^2+52*x+15", "y^2=46*x^6+7*x^5+7*x^4+28*x^3+5*x^2+39*x+5", "y^2=25*x^6+14*x^5+14*x^4+56*x^3+10*x^2+11*x+10", "y^2=49*x^6+9*x^5+5*x^4+45*x^3+21*x^2+6*x+30", "y^2=57*x^6+32*x^5+65*x^4+5*x^3+47*x^2+43*x+54", "y^2=47*x^6+64*x^5+63*x^4+10*x^3+27*x^2+19*x+41", "y^2=50*x^6+29*x^4+49*x^3+19*x^2+x+43", "y^2=33*x^6+58*x^4+31*x^3+38*x^2+2*x+19", "y^2=63*x^6+3*x^5+61*x^4+17*x^3+49*x^2+45*x+45", "y^2=59*x^6+6*x^5+55*x^4+34*x^3+31*x^2+23*x+23", "y^2=50*x^6+19*x^5+49*x^4+61*x^3+47*x^2+17*x+37", "y^2=33*x^6+38*x^5+31*x^4+55*x^3+27*x^2+34*x+7", "y^2=52*x^6+4*x^5+10*x^4+45*x^2+14*x+15", "y^2=42*x^6+8*x^5+26*x^4+14*x^3+14*x^2+13*x+14", "y^2=17*x^6+16*x^5+52*x^4+28*x^3+28*x^2+26*x+28", "y^2=13*x^6+36*x^5+17*x^4+50*x^3+64*x^2+55*x+65", "y^2=26*x^6+5*x^5+34*x^4+33*x^3+61*x^2+43*x+63", "y^2=19*x^6+66*x^5+47*x^4+55*x^3+18*x^2+9*x+12", "y^2=38*x^6+65*x^5+27*x^4+43*x^3+36*x^2+18*x+24", "y^2=37*x^6+18*x^5+27*x^4+3*x^3+51*x^2+27*x+49", "y^2=7*x^6+36*x^5+54*x^4+6*x^3+35*x^2+54*x+31", "y^2=47*x^6+64*x^5+56*x^4+61*x^2+65*x+11", "y^2=19*x^6+39*x^5+30*x^4+48*x^3+56*x^2+x+30", "y^2=61*x^6+21*x^5+16*x^4+27*x^3+28*x^2+44*x+22", "y^2=55*x^6+42*x^5+32*x^4+54*x^3+56*x^2+21*x+44", "y^2=3*x^6+52*x^5+46*x^4+38*x^3+14*x^2+38*x+14", "y^2=26*x^6+29*x^5+21*x^4+55*x^3+37*x^2+52*x+45", "y^2=52*x^6+58*x^5+42*x^4+43*x^3+7*x^2+37*x+23"], "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": 16, "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": 2, "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": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 132, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 132, "label": "2.67.a_n", "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, 0, 13, 0, 4489], "poly_str": "1 0 13 0 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, 0, -121], "simple_distinct": ["1.67.al", "1.67.l"], "simple_factors": ["1.67.alA", "1.67.lA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F-V-7", "7,38*F+36", "11,3*F^2+3*F-19*V+201", "7,46*F-V+41"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.3.1", "splitting_polynomials": [[1, -1, 1]], "twist_count": 24, "twists": [["2.67.aw_jv", "2.4489.ba_nnv", 2], ["2.67.w_jv", "2.4489.ba_nnv", 2], ["2.67.abb_ly", "2.300763.a_ajvta", 3], ["2.67.av_ig", "2.300763.a_ajvta", 3], ["2.67.ag_db", "2.300763.a_ajvta", 3], ["2.67.a_aes", "2.300763.a_ajvta", 3], ["2.67.a_ef", "2.300763.a_ajvta", 3], ["2.67.g_db", "2.300763.a_ajvta", 3], ["2.67.v_ig", "2.300763.a_ajvta", 3], ["2.67.bb_ly", "2.300763.a_ajvta", 3], ["2.67.a_an", "2.20151121.babq_jyabjf", 4], ["2.67.abg_pa", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.aq_hh", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.al_cc", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.ak_gd", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.af_abq", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.f_abq", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.k_gd", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.l_cc", "2.90458382169.atrma_bagkgdypy", 6], ["2.67.q_hh", "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_es", "2.8182718904632857144561.blpvfkjfw_xjhkhpawvmpnyyig", 12]], "weak_equivalence_count": 16, "zfv_index": 23716, "zfv_index_factorization": [[2, 2], [7, 2], [11, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 21609, "zfv_singular_count": 8, "zfv_singular_primes": ["2,F-V-7", "7,38*F+36", "11,3*F^2+3*F-19*V+201", "7,46*F-V+41"]}