Commentary history

1 edit.

Michael Rubinstein · 2026-09-29 19:19:13 UTC

Specialization at t = 5/2 of a rank-17 elliptic K3 family (member P = -3G + theta of C546 in https://gist.github.com/7fff-zip/58764130a98380def8d555e30ba81344, in reduced coordinates y^2 = x^3 - 27*c4(t)*x - 54*c6(t), c4 = 113915556676586218390225 + 117014247072745494659640*t - 714542170231101375740040*t^2 + 59737931954947719760560*t^3 + 1321595301880580949151920*t^4 - 1928468740555818605289600*t^5 + 1536514504542469295299200*t^6 - 464451616236152639846880*t^7 + 46428990309509190682896*t^8, c6 = -38059341830230470571898103643651225 - 60802697439351169215335193049612020*t + 306907782422718633140882412470699604*t^2 + 350452937805251724377651403468219240*t^3 - 963553613419713777812910016932916800*t^4 - 1073907848531523127380729597230188320*t^5 + 2003891611171001180234808501351087840*t^6 + 1925073232043332626346743369726726096*t^7 - 4737928635455002698341677174065585720*t^8 + 3095917488055497753721277439726477600*t^9 - 978774537199645066029066153236296800*t^10 + 155737640585348222809204520763612480*t^11 - 9967046802486275083949405161786944*t^12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).