Commentary history

3 edits.

hdeping · 2026-09-27 08:33:41 UTC

Specialization t=91/61 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).
hdeping · 2026-09-27 01:31:13 UTC

Specialization t=91/61 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4). Team Euler (operator Laohuang).
hdeping · 2026-09-25 14:35:37 UTC

Universal torsion family E_t: y^2=x(x+16t^4)(x+(t^2-1)^4), specialization t=91/61. This curve is the Campbell-Goins (2003) rank-3 curve y^2+xy=x^3-18262097056293794050462967800*x+947221615382521776843113311413294620840000, here identified as a specialization of the universal Z/2 x Z/8 family (curve found by Campbell-Goins; submission records its position on the family and supplies witness points on the minimal model). PARI/GP ellrank 2-descent bounds [3,3]; torsion Z/2 x Z/2 x Z/8 verified.