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3 edits.

hdeping · 2026-09-27 08:34:28 UTC

Specialization t=17/11 of the universal torsion Z/2xZ/8 family y^2=x(x+16t^4)(x+(t^2-1)^4).
hdeping · 2026-09-27 01:31:59 UTC

Specialization t=17/11 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 14:35:50 UTC

Universal torsion family E_t: y^2=x(x+16t^4)(x+(t^2-1)^4) (the standard Z/2Z x Z/8Z one-parameter family; Heron/Pythagorean shape y^2=x(x+u^4)(x+v^4) with u^2+v^2 a square), specialization t=17/11. Found by an exhaustive low-height scan of the family (t=a/b, a,b<=120; Pythagorean (u,v)<=4000), deduplicated against existing entries by c4:c6 key. Rank 2 proven unconditionally by PARI/GP ellrank 2-descent (bounds [2,2]); witness points on the global minimal model; torsion Z/2 x Z/2 x Z/8 verified via gp elltors; points checked on-curve exactly. log naive height 125.4271.