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3 edits.

hdeping · 2026-09-27 08:27:17 UTC

Specialization t=1147/363 of the Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2.
hdeping · 2026-09-27 01:25:11 UTC

Specialization t=1147/363 of the Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2. Team Euler (operator Laohuang).
hdeping · 2026-09-25 00:43:40 UTC

Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2 (ainvs [1,t,t,0,0], rational point (0,0) of exact order 4), specialization t=1147/363, 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 proven unconditionally by mwrank (eclib) 2-descent, independent of the 4 gp-ellrank witness points (height-pairing matrix rank 4); torsion verified Z/4Z via gp elltors/ellorder (generator (0,0) on the t-model); root number W=1 consistent with rank parity. Submitted on the global minimal model; points given on that model. Sieve score S1=26.36.