# Stored data for abelian variety isogeny class 2.41.ad_bc, downloaded from the LMFDB on 15 October 2026.
{"abvar_count": 1584, "abvar_counts": [1584, 2908224, 4740120000, 7997953353984, 13425982155591984, 22562826796984320000, 37929146706520478641584, 63759018571604361431737344, 107178911831200151967698520000, 180167783653047941628995982072384], "abvar_counts_str": "1584 2908224 4740120000 7997953353984 13425982155591984 22562826796984320000 37929146706520478641584 63759018571604361431737344 107178911831200151967698520000 180167783653047941628995982072384 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.251940962052475, 0.655213070720013], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 39, "curve_counts": [39, 1729, 68778, 2830369, 115884879, 4749964558, 194753860599, 7984923683329, 327381875941338, 13422659362051729], "curve_counts_str": "39 1729 68778 2830369 115884879 4749964558 194753860599 7984923683329 327381875941338 13422659362051729 ", "curves": ["y^2=30*x^6+2*x^5+35*x^4+3*x^3+9*x^2+19*x+27", "y^2=12*x^6+22*x^5+28*x^4+28*x^3+16*x^2+x+3", "y^2=21*x^6+29*x^5+6*x^4+2*x^3+27*x^2+36*x+7", "y^2=31*x^6+7*x^5+8*x^4+26*x^3+14*x^2+15*x+26", "y^2=27*x^6+11*x^5+34*x^3+14*x^2+37*x", "y^2=x^6+16*x^5+26*x^4+34*x^3+34*x^2+34*x+12", "y^2=29*x^5+9*x^4+38*x^3+7*x^2+29*x+11", "y^2=33*x^6+x^5+35*x^4+15*x^3+38*x^2+14*x+24", "y^2=11*x^6+33*x^5+19*x^4+14*x^3+26*x^2+32*x+19", "y^2=30*x^6+11*x^4+6*x^2+31*x+33", "y^2=10*x^6+3*x^5+37*x^4+19*x^3+27*x^2+31", "y^2=28*x^6+3*x^5+35*x^4+13*x^3+36*x^2+21*x+12", "y^2=5*x^6+6*x^5+9*x^4+26*x^3+4*x^2+2*x+24", "y^2=38*x^6+28*x^5+8*x^4+4*x^3+23*x+39", "y^2=20*x^6+5*x^5+24*x^4+2*x^3+39*x^2+25*x+19", "y^2=6*x^6+12*x^5+13*x^4+39*x^3+4*x^2+9*x+38", "y^2=39*x^6+20*x^5+40*x^4+8*x^3+6*x^2+7*x+24", "y^2=24*x^6+7*x^5+15*x^4+20*x^3+19*x^2+7*x+15", "y^2=x^6+18*x^5+30*x^4+21*x^3+9*x^2+40*x+4", "y^2=25*x^6+23*x^5+34*x^4+38*x^3+28*x^2+12*x+11", "y^2=17*x^6+4*x^5+27*x^4+38*x^3+x^2+36*x+14", "y^2=34*x^6+10*x^5+23*x^4+24*x^3+36*x^2+34*x+25", "y^2=40*x^6+34*x^5+39*x^3+19*x^2+21*x+6", "y^2=23*x^6+11*x^5+25*x^4+33*x^3+22*x^2+12*x", "y^2=13*x^6+3*x^5+x^4+34*x^3+40*x^2+30*x+39", "y^2=35*x^6+2*x^5+15*x^4+36*x^3+26*x^2+4*x+24", "y^2=30*x^6+12*x^5+24*x^4+2*x^3+28*x^2+28*x+19", "y^2=23*x^6+16*x^5+34*x^4+14*x^3+31*x^2+10*x+38", "y^2=4*x^5+26*x^4+21*x^3+10*x^2+18*x+17", "y^2=24*x^6+3*x^5+10*x^4+25*x^2+18", "y^2=30*x^6+7*x^5+30*x^4+33*x^3+9*x+38", "y^2=5*x^6+13*x^5+20*x^4+34*x^3+23*x+3", "y^2=30*x^6+25*x^5+8*x^4+38*x^3+29*x^2+29*x+32", "y^2=22*x^6+32*x^4+11*x^3+2*x^2+14*x+33", "y^2=x^6+11*x^5+39*x^4+40*x^3+37*x^2+39*x+32", "y^2=13*x^6+34*x^5+34*x^4+28*x^3+26*x^2+25*x+26", "y^2=3*x^6+4*x^5+9*x^4+37*x^3+6*x^2+32*x", "y^2=9*x^6+2*x^5+40*x^4+19*x^3+31*x^2+35*x+17", "y^2=15*x^6+3*x^5+8*x^4+13*x^3+9*x^2+23*x+22", "y^2=31*x^6+34*x^4+12*x^3+12*x^2+17*x+5", "y^2=27*x^6+8*x^5+2*x^4+18*x^2+14*x+1", "y^2=6*x^6+25*x^5+22*x^4+31*x^3+22*x^2+4*x+20", "y^2=33*x^6+25*x^5+22*x^4+29*x^3+16*x^2+39*x+33", "y^2=14*x^6+37*x^5+24*x^4+33*x^3+23*x^2+3*x+5", "y^2=15*x^6+24*x^5+24*x^4+21*x^3+13*x^2+26*x+34", "y^2=37*x^6+14*x^5+2*x^4+17*x^3+21*x^2+6*x+4", "y^2=26*x^6+15*x^5+3*x^4+11*x^3+32*x^2+12*x+21", "y^2=24*x^6+28*x^5+25*x^4+2*x^3+2*x^2+39*x+25", "y^2=26*x^6+38*x^5+11*x^4+6*x^3+10*x^2+28*x+35", "y^2=7*x^6+x^5+15*x^4+6*x^3+23*x^2+11*x", "y^2=18*x^6+16*x^5+35*x^4+8*x^3+5*x^2+6*x+31", "y^2=3*x^6+21*x^5+28*x^4+36*x^3+16*x^2+4*x+4", "y^2=5*x^6+22*x^5+35*x^4+31*x^3+18*x^2+6*x", "y^2=22*x^6+40*x^5+30*x^4+35*x^2+40*x+10", "y^2=16*x^6+12*x^5+5*x^4+29*x^3+4*x^2+17*x+9", "y^2=34*x^6+6*x^5+24*x^4+12*x^3+4*x^2+39*x+26", "y^2=13*x^6+19*x^5+x^4+27*x^3+36*x^2+38*x+13", "y^2=6*x^6+32*x^5+19*x^4+33*x^3+12*x^2+9*x+1", "y^2=2*x^6+4*x^5+22*x^4+30*x^3+31*x^2+17*x+28", "y^2=23*x^6+2*x^5+22*x^4+27*x^3+5*x^2+7*x+33", "y^2=31*x^6+37*x^5+19*x^4+24*x^3+35*x^2+23*x+8", "y^2=4*x^6+29*x^5+30*x^4+40*x^3+24*x^2+16*x+26", "y^2=17*x^6+10*x^5+39*x^4+10*x^3+17*x^2+31*x+9", "y^2=21*x^6+18*x^5+11*x^4+27*x^3+20*x^2+27*x+9", "y^2=24*x^6+5*x^5+16*x^4+22*x^2+14*x+4", "y^2=21*x^6+21*x^5+24*x^4+17*x^3+x^2+10*x+22", "y^2=11*x^6+10*x^5+17*x^4+14*x^3+26*x^2+22*x+25", "y^2=20*x^6+13*x^5+4*x^4+24*x^3+28*x^2+22*x+20", "y^2=23*x^6+21*x^5+32*x^4+32*x^3+25*x^2+36*x+14", "y^2=40*x^6+28*x^5+26*x^4+31*x^2+24*x+22", "y^2=27*x^6+23*x^5+12*x^4+27*x^3+9*x^2+33*x+35", "y^2=29*x^6+2*x^5+39*x^4+35*x^3+40*x^2+9*x+4", "y^2=35*x^6+40*x^5+17*x^4+2*x^2+14*x+34", "y^2=10*x^6+14*x^5+32*x^4+23*x^3+14*x^2+29", "y^2=7*x^6+2*x^5+25*x^4+40*x^3+2*x^2+6*x+26", "y^2=30*x^6+3*x^5+7*x^4+39*x^3+8*x^2+11*x+23", "y^2=9*x^6+29*x^4+17*x^3+17*x^2+29*x+11", "y^2=40*x^6+21*x^5+7*x^4+4*x^3+25*x^2+34*x+35", "y^2=37*x^6+x^5+39*x^4+16*x^3+40*x^2+24*x+4", "y^2=11*x^6+17*x^5+23*x^4+18*x^3+38*x^2+27*x+10", "y^2=33*x^6+8*x^5+17*x^4+36*x^3+9*x^2+12*x+4", "y^2=29*x^6+x^5+38*x^4+21*x^3+3*x^2+13*x+4", "y^2=40*x^6+31*x^5+5*x^4+36*x^3+22*x^2+4*x+4", "y^2=4*x^6+19*x^5+4*x^4+x^3+5*x^2+15*x+36", "y^2=25*x^6+23*x^5+3*x^4+2*x^3+7*x+22", "y^2=3*x^6+24*x^5+19*x^4+28*x^3+40*x^2+25*x+39", "y^2=15*x^6+9*x^5+33*x^4+39*x^3+38*x^2+5*x+3", "y^2=19*x^6+22*x^5+2*x^4+20*x^3+29*x^2+9*x+9", "y^2=26*x^6+37*x^5+14*x^4+40*x^3+17*x^2+16", "y^2=2*x^6+25*x^5+x^4+13*x^3+31*x^2+10*x+19", "y^2=19*x^6+23*x^5+32*x^4+22*x^3+34*x^2+18*x+14", "y^2=24*x^6+27*x^5+33*x^4+36*x^3+24*x^2+40", "y^2=25*x^6+12*x^5+22*x^4+5*x^3+38*x^2+18*x+26", "y^2=27*x^6+4*x^5+10*x^4+4*x^3+12*x^2+21*x+23", "y^2=38*x^6+21*x^5+7*x^4+40*x^3+38*x^2+35*x+22", "y^2=6*x^6+39*x^5+16*x^4+23*x^3+18*x^2+21*x+1", "y^2=22*x^6+5*x^5+31*x^4+39*x^3+23*x^2+34*x+4", "y^2=14*x^6+28*x^5+27*x^4+24*x^3+2*x^2+7*x+23", "y^2=3*x^6+14*x^5+11*x^4+2*x^3+17*x^2+21*x+28", "y^2=32*x^6+13*x^5+36*x^4+10*x^3+38*x^2+39*x+14", "y^2=28*x^6+40*x^5+10*x^4+18*x^3+29*x^2+x+34", "y^2=4*x^6+6*x^5+23*x^4+6*x^3+x^2+34*x+25", "y^2=26*x^6+21*x^5+20*x^4+17*x^2+31*x+35", "y^2=38*x^6+11*x^5+20*x^4+14*x^3+8*x^2+22*x+24", "y^2=4*x^6+24*x^5+40*x^4+23*x^3+32*x^2+10*x+13", "y^2=17*x^6+21*x^5+13*x^4+27*x^2+26*x+7", "y^2=37*x^6+7*x^5+33*x^4+38*x^3+31*x^2+30*x+34", "y^2=30*x^6+31*x^5+34*x^4+34*x^3+2*x^2+18*x+6", "y^2=37*x^6+x^5+21*x^4+38*x^3+10*x^2+27*x+8", "y^2=10*x^6+38*x^5+32*x^4+14*x^3+37*x^2+2", "y^2=35*x^6+38*x^5+11*x^4+21*x^3+15*x^2+33*x+33", "y^2=24*x^6+29*x^5+11*x^4+12*x^3+18*x^2+28*x+36", "y^2=18*x^6+40*x^5+17*x^4+10*x^3+31*x^2+15*x+21", "y^2=21*x^6+34*x^5+38*x^4+12*x^3+38*x^2+14*x+13", "y^2=37*x^6+36*x^5+13*x^4+37*x^3+4*x^2+40*x+24", "y^2=6*x^6+34*x^5+15*x^4+25*x^3+5*x^2+24*x+13", "y^2=8*x^6+7*x^5+21*x^4+20*x^3+34*x^2+30*x+34", "y^2=23*x^6+32*x^5+5*x^4+20*x^3+29*x^2+35*x+11", "y^2=21*x^6+37*x^5+39*x^4+9*x^3+36*x^2+3*x+15", "y^2=10*x^6+15*x^5+20*x^4+39*x^3+6*x^2+3*x", "y^2=x^5+9*x^4+4*x^3+7*x^2+35*x+33", "y^2=35*x^6+19*x^5+2*x^4+23*x^2+32*x+20", "y^2=38*x^6+18*x^5+25*x^4+37*x^3+32*x^2+19*x+28", "y^2=22*x^6+6*x^5+23*x^4+17*x^3+22*x^2+17*x+11", "y^2=27*x^6+34*x^5+15*x^3+5*x^2+6*x+9", "y^2=8*x^6+2*x^5+11*x^4+40*x^3+x^2+36*x+6", "y^2=37*x^6+3*x^5+26*x^4+31*x^3+5*x^2+10*x+17", "y^2=25*x^6+30*x^5+28*x^4+32*x^3+30*x^2+15*x+11", "y^2=27*x^6+9*x^5+9*x^4+26*x^3+28*x^2+35*x+20", "y^2=14*x^5+21*x^4+20*x^3+17*x^2+11*x+17", "y^2=32*x^6+30*x^5+19*x^4+35*x^3+7*x^2+25*x+26", "y^2=40*x^6+25*x^5+22*x^4+38*x^3+11*x^2+15*x+34", "y^2=23*x^6+34*x^5+39*x^4+14*x^3+36*x^2+3*x", "y^2=4*x^6+20*x^5+11*x^4+5*x^3+16*x^2+7*x+34", "y^2=19*x^6+13*x^5+39*x^4+30*x^3+18*x^2+14*x+26", "y^2=20*x^6+22*x^5+23*x^4+37*x^3+10*x^2+7*x+35", "y^2=26*x^6+21*x^5+16*x^4+37*x^3+21*x^2+19*x+20", "y^2=13*x^5+3*x^4+26*x^3+5*x+25", "y^2=38*x^6+37*x^5+39*x^4+34*x^3+36*x^2+10*x+17", "y^2=6*x^6+26*x^5+30*x^4+34*x^3+17*x^2+34*x+36", "y^2=x^6+x^5+24*x^4+38*x^3+33*x^2+4*x+15", "y^2=3*x^6+16*x^5+18*x^4+17*x^3+33*x^2+16*x+30", "y^2=8*x^6+28*x^5+3*x^4+2*x^3+34*x^2+7*x+12", "y^2=25*x^6+40*x^5+14*x^4+16*x^3+16*x^2+25*x+21", "y^2=8*x^6+10*x^5+18*x^4+36*x^3+36*x^2+22*x+32", "y^2=26*x^6+5*x^5+10*x^4+33*x^3+27*x^2+6*x+5", "y^2=13*x^6+3*x^5+7*x^4+24*x^3+39*x^2+6*x", "y^2=28*x^6+27*x^5+34*x^4+22*x^3+37*x^2+32*x+24", "y^2=32*x^6+8*x^5+8*x^4+21*x^3+18*x^2+19*x+7", "y^2=9*x^6+33*x^5+4*x^4+8*x^3+21*x^2+10*x+17", "y^2=2*x^6+15*x^5+6*x^4+16*x^3+x^2+37*x+18", "y^2=14*x^6+21*x^5+2*x^4+22*x^3+14*x^2+4", "y^2=18*x^6+x^5+36*x^4+21*x^3+16*x^2+2*x+18", "y^2=29*x^6+38*x^5+5*x^4+34*x^3+8*x^2+x+14", "y^2=38*x^6+6*x^5+32*x^4+32*x^3+11*x^2+27*x+25", "y^2=40*x^6+35*x^5+24*x^4+23*x^3+10*x^2+17*x+21", "y^2=30*x^6+10*x^5+18*x^4+2*x^3+24*x^2+12*x+31", "y^2=7*x^6+18*x^5+40*x^4+20*x^3+31*x^2+5*x+30", "y^2=24*x^6+30*x^5+40*x^4+11*x^3+13*x^2+34*x", "y^2=37*x^6+36*x^5+24*x^4+13*x^3+x^2+3*x+26", "y^2=22*x^5+6*x^4+21*x^3+15*x^2+36*x+21", "y^2=15*x^6+38*x^5+23*x^4+38*x^3+23*x+20", "y^2=35*x^6+32*x^5+30*x^4+33*x^3+7*x^2+19*x+1", "y^2=33*x^6+37*x^5+3*x^4+32*x^3+18*x^2+34*x+1", "y^2=31*x^6+22*x^5+10*x^4+32*x^3+15*x^2+32*x+14", "y^2=21*x^6+40*x^4+20*x^3+9*x^2+39*x+2", "y^2=36*x^6+15*x^5+40*x^4+4*x^3+20*x^2+35*x+12", "y^2=32*x^6+15*x^5+28*x^4+9*x^3+34*x^2+23*x+19", "y^2=36*x^6+9*x^5+22*x^4+22*x^3+15*x^2+7*x+33", "y^2=29*x^6+26*x^5+7*x^4+17*x^3+31*x^2+10*x+17", "y^2=9*x^6+20*x^5+x^4+26*x^3+10*x^2+35*x+5", "y^2=13*x^6+36*x^5+23*x^4+12*x^2+31*x+31", "y^2=31*x^6+10*x^5+40*x^4+3*x^2+8*x+9", "y^2=39*x^6+27*x^5+26*x^4+9*x^3+28*x^2+9*x+40", "y^2=12*x^6+30*x^5+4*x^4+40*x^3+3*x^2+x+6", "y^2=36*x^6+15*x^5+10*x^4+22*x^3+27*x^2+11*x+31", "y^2=13*x^6+33*x^5+29*x^4+15*x^3+25*x^2+39*x+12", "y^2=9*x^6+15*x^4+4*x^3+20*x^2+39*x+34", "y^2=23*x^6+3*x^5+38*x^4+11*x^3+12*x^2+27*x+29", "y^2=38*x^6+15*x^5+17*x^4+31*x^3+24*x^2+22*x+31", "y^2=32*x^6+3*x^5+13*x^4+11*x^3+26*x+17", "y^2=29*x^6+12*x^5+35*x^4+25*x^3+32*x^2+33*x+8", "y^2=5*x^6+31*x^5+20*x^4+32*x^3+16*x^2+32*x+34", "y^2=8*x^6+26*x^5+34*x^4+26*x^3+16*x^2+40*x+28", "y^2=29*x^6+30*x^5+9*x^4+40*x^3+27*x^2+17*x", "y^2=15*x^6+23*x^4+3*x^3+20*x^2+6*x+26", "y^2=24*x^6+17*x^5+26*x^4+14*x^3+25*x^2+3*x+21", "y^2=36*x^6+11*x^5+25*x^4+29*x^3+22*x^2+9*x+2", "y^2=39*x^6+29*x^5+16*x^4+10*x^3+25*x^2+2*x+19", "y^2=21*x^6+26*x^5+16*x^4+3*x^3+16*x^2+21*x+35", "y^2=26*x^6+35*x^5+38*x^4+32*x^3+13*x^2+18*x+39", "y^2=33*x^6+35*x^5+5*x^4+24*x^3+18*x^2+10*x+4", "y^2=8*x^6+21*x^5+28*x^4+2*x^3+2*x^2+37*x+5", "y^2=10*x^5+34*x^4+7*x^3+39*x^2+3*x+15", "y^2=20*x^6+26*x^5+36*x^4+33*x^3+2*x^2+10*x+37", "y^2=11*x^6+35*x^5+29*x^4+21*x^3+19*x^2+11*x+22", "y^2=31*x^6+13*x^5+31*x^4+36*x^3+30*x^2+30*x+39", "y^2=35*x^6+20*x^5+15*x^4+36*x^3+37*x^2+14", "y^2=2*x^6+30*x^5+14*x^4+38*x^3+40*x^2+6*x+4", "y^2=3*x^6+20*x^5+24*x^4+16*x^3+22*x^2+6", "y^2=11*x^6+37*x^5+23*x^4+31*x^3+13*x^2+36*x+26", "y^2=31*x^6+20*x^5+38*x^4+19*x^3+39*x^2+26*x+39", "y^2=25*x^6+38*x^5+20*x^4+29*x^3+26*x^2+7*x+1", "y^2=20*x^6+34*x^5+39*x^4+10*x^3+20*x^2+5*x+35", "y^2=28*x^6+31*x^5+9*x^4+4*x^3+20*x^2+39*x+5", "y^2=26*x^6+19*x^5+37*x^3+8*x^2+14*x+31", "y^2=5*x^6+11*x^5+4*x^4+22*x^3+18*x^2+33*x+27", "y^2=17*x^6+9*x^4+6*x^3+38*x^2+12*x+37", "y^2=18*x^5+17*x^4+5*x^3+23*x^2+3*x+12", "y^2=13*x^6+13*x^5+21*x^3+x^2+18*x+8"], "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": 24, "g": 2, "galois_groups": ["2T1", "2T1"], "geom_dim1_distinct": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.83.1", "2.0.8.1"], "geometric_splitting_field": "4.0.440896.1", "geometric_splitting_polynomials": [[363, -46, 47, -2, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 210, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 210, "label": "2.41.ad_bc", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2, 3], "number_fields": ["2.0.83.1", "2.0.8.1"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -3, 28, -123, 1681], "poly_str": "1 -3 28 -123 1681 ", "primitive_models": [], "q": 41, "real_poly": [1, -3, -54], "simple_distinct": ["1.41.aj", "1.41.g"], "simple_factors": ["1.41.ajA", "1.41.gA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,V+8", "3,-13*F-5", "5,67*F+2*V-8", "2,F-11"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.440896.1", "splitting_polynomials": [[363, -46, 47, -2, 1]], "twist_count": 4, "twists": [["2.41.ap_fg", "2.1681.bv_fbc", 2], ["2.41.d_bc", "2.1681.bv_fbc", 2], ["2.41.p_fg", "2.1681.bv_fbc", 2]], "weak_equivalence_count": 24, "zfv_index": 900, "zfv_index_factorization": [[2, 2], [3, 2], [5, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 10624, "zfv_singular_count": 8, "zfv_singular_primes": ["3,V+8", "3,-13*F-5", "5,67*F+2*V-8", "2,F-11"]}