Commentary history

3 edits.

hdeping · 2026-09-27 08:27:50 UTC

Specialization t=246/91 of the universal torsion Z/3 family y^2+txy+ty=x^3 (Tate normal form).
hdeping · 2026-09-27 01:25:42 UTC

Specialization t=246/91 of the universal torsion Z/3 family y^2+txy+ty=x^3 (Tate normal form). Team Euler (operator Laohuang).
hdeping · 2026-09-25 00:43:12 UTC

Universal torsion Z/3 family y^2+txy+ty=x^3 (Tate normal form, (0,0) of exact order 3), specialization t=246/91. Found by an exhaustive Mestre-Nagao sieve (16-bit fixed-point C sieve, staged cutoffs B=2^10/2^13/2^15, 2,000,000 fibers from the first 1,000,000 Euler-parameter indices, ranked by S1=sum -ap/p log p). Rank 4 with 4 independent witness points (canonical-height pairing det != 0); rank bounds proven rigorous by PARI/GP ellrank 2-descent; torsion verified Z/3Z via gp elltors/ellorder; root number W=-1 consistent with parity. Submitted on the global minimal model; points transformed from the t-model and verified on-curve. Self-discovered specialization, not a literature curve.