# Stored data for abelian variety isogeny class 2.67.as_hi, downloaded from the LMFDB on 02 September 2025.
{"abvar_count": 3456, "abvar_counts": [3456, 20404224, 90702654336, 406071480877056, 1822834862019236736, 8182777752727385020416, 36732277978356595546924416, 164890970850407351987343458304, 740195505006845724362088957389184, 3322737654548770551732342266247911424], "abvar_counts_str": "3456 20404224 90702654336 406071480877056 1822834862019236736 8182777752727385020416 36732277978356595546924416 164890970850407351987343458304 740195505006845724362088957389184 3322737654548770551732342266247911424 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.173442769152047, 0.421429069537878], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 50, "curve_counts": [50, 4546, 301574, 20151310, 1350122930, 90459032722, 6060720319718, 406067707340254, 27206534071007858, 1822837800626938786], "curve_counts_str": "50 4546 301574 20151310 1350122930 90459032722 6060720319718 406067707340254 27206534071007858 1822837800626938786 ", "curves": ["y^2=52*x^6+23*x^5+62*x^4+29*x^3+38*x^2+18*x+59", "y^2=30*x^6+17*x^5+40*x^4+26*x^3+29*x^2+36*x+43", "y^2=13*x^6+57*x^5+58*x^4+58*x^3+30*x^2+20*x+57", "y^2=47*x^6+32*x^5+22*x^4+9*x^3+3*x^2+49*x+51", "y^2=58*x^6+33*x^5+17*x^4+11*x^3+22*x^2+30*x+55", "y^2=34*x^6+57*x^5+x^4+x^3+47*x^2+48*x+55", "y^2=2*x^6+44*x^5+30*x^4+20*x^3+2*x^2+9*x+34", "y^2=32*x^6+65*x^5+39*x^3+46*x^2+63*x+1", "y^2=52*x^6+30*x^5+17*x^4+42*x^3+48*x^2+61*x+29", "y^2=63*x^6+25*x^5+x^4+22*x^3+x^2+25*x+63", "y^2=5*x^6+44*x^5+2*x^4+30*x^3+7*x^2+47*x+5", "y^2=61*x^6+64*x^5+34*x^4+46*x^3+12*x^2+16*x+65", "y^2=13*x^6+14*x^5+10*x^4+36*x^2+26*x+18", "y^2=20*x^6+12*x^5+x^4+29*x^3+26*x^2+32*x+48", "y^2=2*x^6+15*x^5+37*x^4+4*x^3+6*x^2+2*x+40", "y^2=55*x^6+46*x^5+2*x^4+30*x^3+53*x^2+47*x+30", "y^2=12*x^6+51*x^5+6*x^4+43*x^3+20*x^2+14*x+18", "y^2=46*x^6+2*x^5+34*x^4+42*x^3+9*x^2+23*x+41", "y^2=4*x^6+35*x^5+65*x^4+2*x^3+65*x^2+35*x+4", "y^2=24*x^6+45*x^5+3*x^4+29*x^3+38*x^2+9*x+23", "y^2=7*x^6+31*x^5+5*x^4+x^3+37*x^2+14*x+15", "y^2=48*x^6+64*x^5+36*x^4+39*x^3+41*x^2+58*x+61", "y^2=13*x^6+2*x^5+65*x^4+29*x^3+30*x^2+42*x+63", "y^2=59*x^6+52*x^5+65*x^4+8*x^3+11*x^2+39*x+1", "y^2=20*x^6+41*x^5+25*x^4+63*x^3+45*x^2+12*x+24", "y^2=44*x^6+48*x^5+27*x^4+39*x^3+49*x^2+55*x+8", "y^2=60*x^6+57*x^5+7*x^4+54*x^3+58*x^2+38*x+15", "y^2=61*x^6+11*x^5+32*x^4+2*x^3+50*x^2+28*x+63", "y^2=58*x^6+50*x^5+28*x^4+64*x^3+28*x^2+50*x+58", "y^2=4*x^6+23*x^5+46*x^4+46*x^3+44*x^2+56*x+33", "y^2=50*x^6+23*x^5+30*x^4+30*x^3+55*x^2+14*x+45", "y^2=15*x^6+30*x^5+25*x^4+54*x^3+18*x^2+43*x+48", "y^2=3*x^6+54*x^5+39*x^4+11*x^3+60*x^2+59*x+25", "y^2=11*x^6+x^5+3*x^4+66*x^3+32*x^2+7*x+55", "y^2=37*x^6+38*x^5+59*x^4+58*x^3+58*x^2+3*x+45", "y^2=4*x^6+57*x^5+2*x^4+32*x^3+66*x^2+26*x+4", "y^2=59*x^6+4*x^5+42*x^4+26*x^3+47*x^2+50*x+33", "y^2=58*x^6+18*x^5+41*x^4+28*x^3+58*x^2+8*x+54", "y^2=63*x^6+33*x^5+11*x^4+8*x^3+59*x^2+19*x+2", "y^2=53*x^6+15*x^5+16*x^4+63*x^3+37*x^2+11*x+34", "y^2=30*x^6+20*x^5+47*x^4+12*x^3+43*x^2+50*x+60", "y^2=8*x^6+3*x^5+47*x^4+24*x^3+4*x^2+30*x+18", "y^2=26*x^6+58*x^5+28*x^4+59*x^3+50*x^2+52*x+43", "y^2=34*x^6+31*x^5+65*x^4+59*x^3+46*x+29", "y^2=15*x^6+40*x^5+56*x^4+18*x^3+12*x^2+41*x+21", "y^2=45*x^6+33*x^5+52*x^4+6*x^3+54*x^2+43*x+13", "y^2=12*x^6+25*x^5+55*x^4+33*x^3+19*x^2+65*x+31", "y^2=35*x^6+47*x^5+55*x^4+47*x^3+46*x^2+20*x+50", "y^2=34*x^6+22*x^5+40*x^4+30*x^3+31*x^2+20*x+29", "y^2=42*x^6+62*x^5+52*x^4+47*x^3+23*x^2+12*x+4", "y^2=46*x^6+16*x^5+28*x^4+57*x^3+15*x^2+60*x+30", "y^2=22*x^6+66*x^5+x^4+23*x^3+37*x^2+65*x+40", "y^2=42*x^6+36*x^5+25*x^4+44*x^3+22*x^2+41*x+22", "y^2=39*x^6+46*x^5+33*x^4+58*x^3+33*x^2+46*x+39", "y^2=34*x^6+7*x^5+12*x^4+51*x^3+24*x^2+13*x+1", "y^2=53*x^6+19*x^5+40*x^4+34*x^3+15*x^2+61*x+21", "y^2=13*x^6+59*x^5+7*x^4+61*x^3+33*x+8", "y^2=20*x^6+15*x^5+7*x^4+51*x^3+30*x^2+54*x+31", "y^2=47*x^6+5*x^5+65*x^4+63*x^3+38*x^2+6*x+8", "y^2=51*x^6+46*x^5+54*x^4+62*x^3+4*x^2+42*x+55", "y^2=66*x^6+18*x^5+12*x^4+20*x^3+51*x^2+25*x+48", "y^2=39*x^6+50*x^5+53*x^4+21*x^3+63*x^2+56*x+53", "y^2=11*x^6+31*x^5+52*x^4+32*x^3+52*x^2+31*x+11", "y^2=63*x^6+31*x^5+x^4+56*x^3+62*x^2+38*x+31", "y^2=43*x^6+21*x^5+47*x^4+66*x^3+20*x^2+19*x+30", "y^2=46*x^6+10*x^5+15*x^3+53*x^2+30*x+42", "y^2=63*x^6+29*x^5+12*x^4+49*x^3+41*x^2+66*x+27", "y^2=3*x^6+26*x^5+37*x^4+12*x^3+22*x^2+27*x+27", "y^2=41*x^6+2*x^5+21*x^4+33*x^3+52*x^2+10*x+43", "y^2=20*x^6+42*x^5+30*x^4+16*x^3+61*x^2+55*x+4", "y^2=31*x^6+24*x^5+30*x^4+37*x^3+4*x^2+43*x+13", "y^2=51*x^6+58*x^5+21*x^4+63*x^3+53*x^2+63*x+58", "y^2=61*x^6+42*x^5+24*x^4+15*x^3+23*x^2+4*x+60", "y^2=53*x^6+26*x^5+17*x^4+19*x^3+x^2+50*x+56", "y^2=49*x^6+61*x^5+60*x^4+47*x^3+66*x^2+42*x+21", "y^2=45*x^6+18*x^5+20*x^4+43*x^3+8*x^2+27*x+27", "y^2=7*x^6+55*x^5+66*x^4+33*x^3+53*x^2+63*x+66", "y^2=31*x^6+36*x^5+52*x^4+42*x^3+46*x^2+18*x+64", "y^2=50*x^6+36*x^5+41*x^4+11*x^3+49*x^2+21*x+63", "y^2=7*x^6+17*x^5+49*x^4+4*x^3+26*x^2+42*x+45", "y^2=35*x^6+11*x^5+40*x^4+31*x^3+53*x^2+62*x+1", "y^2=x^6+19*x^5+19*x^4+15*x^3+16*x^2+9*x+7", "y^2=54*x^6+25*x^5+7*x^4+24*x^3+60*x^2+24*x+46", "y^2=43*x^6+14*x^5+45*x^4+50*x^3+3*x^2+62*x+58", "y^2=40*x^6+48*x^5+45*x^4+52*x^3+52*x^2+11*x+63", "y^2=30*x^6+10*x^5+x^4+18*x^3+50*x^2+38*x+5", "y^2=26*x^6+18*x^5+54*x^4+66*x^3+27*x^2+65*x+65", "y^2=43*x^6+4*x^5+x^4+43*x^3+66*x^2+62*x+57", "y^2=58*x^6+3*x^5+7*x^4+37*x^3+7*x^2+3*x+58", "y^2=52*x^6+22*x^5+29*x^4+15*x^3+31*x^2+14*x+58", "y^2=48*x^6+40*x^5+15*x^4+23*x^3+22*x^2+25*x+44", "y^2=28*x^6+39*x^5+53*x^4+11*x^3+45*x^2+47*x+5", "y^2=8*x^6+9*x^5+65*x^4+55*x^3+30*x+26", "y^2=19*x^6+60*x^5+38*x^4+42*x^3+62*x^2+43*x+21", "y^2=49*x^6+36*x^4+24*x^3+10*x^2+61*x+6", "y^2=2*x^6+x^5+10*x^4+59*x^3+44*x^2+58*x+50", "y^2=3*x^6+52*x^5+62*x^4+24*x^3+45*x^2+2*x", "y^2=17*x^6+31*x^5+34*x^4+57*x^3+63*x^2+63*x+56", "y^2=43*x^6+14*x^5+21*x^4+14*x^3+29*x^2+24*x+46", "y^2=53*x^6+3*x^5+60*x^4+40*x^3+33*x^2+53*x+27", "y^2=42*x^6+66*x^5+51*x^4+39*x^3+6*x^2+44*x+1", "y^2=29*x^6+52*x^5+57*x^4+58*x^3+41*x^2+15*x+6", "y^2=45*x^6+28*x^5+65*x^4+29*x^3+7*x^2+5*x+58", "y^2=20*x^6+61*x^5+48*x^4+16*x^3+28*x^2+29*x+6", "y^2=39*x^6+61*x^5+20*x^4+50*x^3+44*x^2+46*x+39", "y^2=41*x^6+49*x^5+45*x^4+41*x^3+29*x^2+31*x+29", "y^2=46*x^6+53*x^5+4*x^4+12*x^3+46*x^2+53*x+45", "y^2=27*x^6+18*x^5+59*x^4+36*x^3+40*x^2+25*x+32", "y^2=27*x^6+32*x^5+18*x^4+7*x^3+48*x^2+34*x+31", "y^2=47*x^6+39*x^5+20*x^4+49*x^3+28*x^2+30*x+8", "y^2=45*x^6+16*x^5+34*x^4+28*x^3+20*x^2+64*x+30", "y^2=11*x^6+42*x^5+40*x^4+49*x^3+25*x^2+55*x+41", "y^2=13*x^6+38*x^5+3*x^4+46*x^3+17*x^2+58*x+23", "y^2=65*x^6+5*x^5+13*x^4+60*x^3+23*x^2+11*x+2", "y^2=4*x^6+61*x^5+48*x^4+10*x^3+22*x^2+66*x+25", "y^2=40*x^6+27*x^5+25*x^4+42*x^3+58*x^2+66*x+58", "y^2=26*x^6+58*x^5+44*x^4+19*x^3+42*x^2+5*x+2", "y^2=2*x^6+15*x^5+66*x^4+66*x^3+66*x^2+15*x+2", "y^2=37*x^6+x^5+33*x^4+9*x^3+41*x^2+52*x+30", "y^2=45*x^6+46*x^5+43*x^4+14*x^3+43*x^2+46*x+45", "y^2=25*x^6+19*x^5+52*x^4+56*x^3+32*x^2+29*x+41", "y^2=41*x^6+25*x^5+28*x^4+46*x^3+x^2+34*x+3", "y^2=20*x^6+28*x^5+60*x^3+28*x+20", "y^2=52*x^6+59*x^5+55*x^4+63*x^3+26*x^2+20*x+39", "y^2=7*x^6+2*x^5+40*x^4+41*x^3+63*x^2+26*x+53", "y^2=19*x^6+11*x^5+61*x^4+63*x^3+8*x^2+8*x+31", "y^2=49*x^6+33*x^5+53*x^4+8*x^3+53*x^2+33*x+49", "y^2=49*x^6+34*x^5+21*x^4+41*x^3+38*x^2+49*x+7", "y^2=18*x^6+28*x^5+29*x^4+29*x^2+28*x+18", "y^2=51*x^6+33*x^5+2*x^4+50*x^3+2*x^2+33*x+51", "y^2=28*x^6+22*x^5+45*x^4+57*x^3+30*x^2+58*x+12", "y^2=32*x^6+38*x^5+57*x^4+37*x^3+12*x^2+44*x+31", "y^2=46*x^6+60*x^5+50*x^4+38*x^3+28*x^2+62*x+41", "y^2=8*x^6+42*x^5+11*x^4+25*x^3+39*x^2+61*x+63", "y^2=15*x^6+9*x^5+37*x^4+55*x^3+66*x^2+27*x+46", "y^2=54*x^6+3*x^5+x^4+8*x^3+39*x^2+4*x+27", "y^2=26*x^6+45*x^5+24*x^4+61*x^3+45*x^2+22*x+66", "y^2=8*x^6+52*x^5+16*x^4+23*x^3+50*x^2+3*x+62", "y^2=36*x^6+60*x^5+3*x^4+10*x^3+31*x^2+64*x+35", "y^2=61*x^6+30*x^5+26*x^4+6*x^3+56*x^2+22*x", "y^2=23*x^6+38*x^5+9*x^4+49*x^3+47*x^2+23*x+11", "y^2=43*x^6+30*x^5+34*x^4+43*x^3+34*x^2+30*x+43", "y^2=13*x^6+43*x^5+30*x^4+60*x^3+20*x^2+18*x+44", "y^2=38*x^6+45*x^5+16*x^4+38*x^3+33*x^2+20*x+46", "y^2=50*x^6+62*x^5+58*x^4+4*x^3+66*x^2+63*x+36", "y^2=65*x^6+28*x^5+2*x^4+5*x^3+2*x^2+28*x+65", "y^2=53*x^6+48*x^5+22*x^4+21*x^3+22*x^2+48*x+53", "y^2=19*x^6+18*x^5+64*x^4+29*x^3+54*x^2+10*x+25", "y^2=5*x^6+x^5+33*x^4+56*x^3+23*x^2+x+58", "y^2=49*x^6+7*x^5+6*x^3+63*x^2+18*x+46", "y^2=41*x^6+43*x^5+54*x^4+41*x^3+50*x^2+6*x+46", "y^2=31*x^6+26*x^5+62*x^4+48*x^3+59*x^2+43*x+32", "y^2=22*x^6+31*x^5+45*x^4+9*x^3+53*x^2+52*x+24", "y^2=32*x^6+46*x^5+x^4+64*x^3+35*x^2+12*x+49", "y^2=48*x^6+8*x^5+48*x^4+41*x^3+66*x^2+20*x+31", "y^2=21*x^6+21*x^5+41*x^4+56*x^3+59*x^2+14*x+11", "y^2=51*x^6+62*x^5+20*x^4+32*x^3+63*x^2+55*x+59", "y^2=32*x^6+58*x^5+12*x^4+64*x^3+6*x^2+11*x+12", "y^2=32*x^6+2*x^5+4*x^3+32*x^2+57*x+25", "y^2=13*x^6+34*x^5+22*x^4+50*x^3+15*x^2+15*x+28", "y^2=36*x^6+30*x^5+30*x^4+59*x^3+60*x^2+65", "y^2=58*x^6+22*x^5+11*x^4+38*x^3+x^2+42*x+44", "y^2=32*x^6+58*x^5+66*x^4+42*x^3+30*x^2+2*x+32", "y^2=58*x^6+30*x^5+10*x^4+60*x^3+24*x^2+14*x+32", "y^2=50*x^6+4*x^5+58*x^4+7*x^3+37*x^2+65*x+12", "y^2=61*x^6+27*x^5+53*x^4+53*x^3+22*x^2+60*x+60", "y^2=34*x^6+3*x^5+60*x^4+57*x^3+15*x^2+56*x+7", "y^2=24*x^6+17*x^5+18*x^4+45*x^3+37*x^2+60*x+18", "y^2=57*x^6+59*x^5+46*x^4+35*x^3+11*x^2+30*x+63", "y^2=52*x^6+32*x^5+15*x^4+51*x^3+51*x^2+45*x+34", "y^2=53*x^6+47*x^5+49*x^4+9*x^3+58*x^2+18*x+48", "y^2=40*x^6+9*x^5+40*x^4+48*x^3+7*x^2+61*x+51", "y^2=32*x^6+66*x^5+16*x^4+43*x^3+44*x^2+64*x+12", "y^2=58*x^6+61*x^5+65*x^4+52*x^3+56*x^2+49*x+14", "y^2=63*x^6+47*x^5+29*x^4+x^3+64*x^2+13*x+24", "y^2=27*x^6+10*x^5+5*x^4+51*x^3+35*x^2+10*x+51", "y^2=63*x^6+24*x^5+42*x^4+15*x^3+16*x^2+52*x+50", "y^2=2*x^6+41*x^5+44*x^4+25*x^3+55*x^2+9*x+43", "y^2=45*x^6+39*x^5+50*x^4+44*x^3+13*x^2+28*x+51", "y^2=40*x^6+7*x^5+63*x^4+28*x^3+30*x^2+42*x+9", "y^2=35*x^6+47*x^5+8*x^4+3*x^3+28*x^2+21*x+3", "y^2=x^6+20*x^5+6*x^4+51*x^3+56*x^2+5*x+7", "y^2=3*x^6+29*x^5+32*x^4+22*x^3+30*x^2+12*x+36", "y^2=2*x^6+28*x^5+14*x^4+17*x^3+34*x^2+29*x+51", "y^2=18*x^6+38*x^5+44*x^4+17*x^3+45*x+29", "y^2=4*x^6+8*x^5+64*x^4+66*x^3+33*x^2+54*x+6", "y^2=66*x^6+17*x^5+44*x^4+55*x^3+55*x^2+39*x+21", "y^2=58*x^6+45*x^5+23*x^4+46*x^3+21*x^2+66*x+54", "y^2=29*x^6+21*x^5+21*x^4+65*x^3+17*x^2+29*x+49", "y^2=61*x^6+9*x^5+65*x^4+x^3+21*x^2+24*x+51", "y^2=15*x^6+58*x^5+43*x^4+51*x^3+45*x^2+35*x+55", "y^2=20*x^6+27*x^5+50*x^4+61*x^3+49*x^2+6*x+30", "y^2=17*x^6+42*x^5+58*x^4+59*x^3+2*x^2+24*x+41", "y^2=15*x^6+47*x^5+30*x^4+19*x^3+34*x^2+16*x+40", "y^2=46*x^6+51*x^5+66*x^4+x^3+21*x^2+37*x+63", "y^2=50*x^6+8*x^5+33*x^4+37*x^3+9*x^2+58*x+57", "y^2=52*x^6+22*x^5+61*x^4+45*x^3+64*x^2+16*x+65", "y^2=42*x^6+15*x^5+58*x^4+14*x^3+52*x^2+9*x+29", "y^2=2*x^6+56*x^5+10*x^4+31*x^3+32*x^2+10*x+56", "y^2=20*x^6+30*x^5+64*x^4+11*x^3+51*x^2+50*x+14", "y^2=33*x^6+57*x^5+36*x^4+54*x^3+43*x^2+15*x+37", "y^2=21*x^6+8*x^5+46*x^4+28*x^3+29*x^2+42*x+30", "y^2=35*x^6+13*x^5+50*x^4+49*x^3+30*x^2+38*x+52", "y^2=50*x^6+6*x^5+56*x^4+x^3+41*x^2+32*x+31", "y^2=42*x^6+19*x^5+30*x^4+58*x^3+9*x^2+8*x+3", "y^2=2*x^6+46*x^5+7*x^4+66*x^3+61*x^2+25*x+52", "y^2=41*x^6+62*x^5+17*x^4+33*x^3+48*x^2+32*x+27", "y^2=25*x^6+17*x^5+63*x^4+58*x^3+15*x^2+53*x+49", "y^2=54*x^6+36*x^5+51*x^4+30*x^3+50*x^2+45*x+12", "y^2=42*x^6+22*x^5+58*x^4+51*x^3+65*x^2+17*x+30"], "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": 48, "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": ["2.0.8.1", "2.0.7.1"], "geometric_splitting_field": "4.0.3136.2", "geometric_splitting_polynomials": [[2, -8, 9, -2, 1]], "group_structure_count": 8, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 210, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 210, "label": "2.67.as_hi", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.8.1", "2.0.7.1"], "p": 67, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -18, 190, -1206, 4489], "poly_str": "1 -18 190 -1206 4489 ", "primitive_models": [], "q": 67, "real_poly": [1, -18, 56], "simple_distinct": ["1.67.ao", "1.67.ae"], "simple_factors": ["1.67.aoA", "1.67.aeA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,5*V-41", "3,F-10", "5,2*F^2+16*F-V+53", "3,13*F-2"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.3136.2", "splitting_polynomials": [[2, -8, 9, -2, 1]], "twist_count": 4, "twists": [["2.67.ak_da", "2.4489.ce_cly", 2], ["2.67.k_da", "2.4489.ce_cly", 2], ["2.67.s_hi", "2.4489.ce_cly", 2]], "weak_equivalence_count": 56, "zfv_index": 1800, "zfv_index_factorization": [[2, 3], [3, 2], [5, 2]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 18144, "zfv_singular_count": 8, "zfv_singular_primes": ["2,5*V-41", "3,F-10", "5,2*F^2+16*F-V+53", "3,13*F-2"]}