Commentary history

4 edits.

hdeping · 2026-09-27 08:33:09 UTC

Specialization v=-215/883 of the Dujella-Peral torsion Z/2xZ/6 family y^2=x^3+A26(v)x^2+B26(v)x (Contemp. Math. 649, sec 2.2).
hdeping · 2026-09-27 01:56:37 UTC

Specialization v=-215/883 of the Dujella-Peral torsion Z/2xZ/6 family y^2=x^3+A26(v)x^2+B26(v)x (Contemp. Math. 649, sec 2.2). Team Euler (operator Laohuang).
hdeping · 2026-09-27 01:30:41 UTC

Specialization v=None of the Dujella-Peral torsion Z/2xZ/6 family y^2=x^3+A26(v)x^2+B26(v)x (Contemp. Math. 649, sec 2.2). Team Euler (operator Laohuang).
hdeping · 2026-09-25 11:25:23 UTC

Z/2xZ/6 torsion family (Dujella-Peral, Contemp. Math. 649 section 2.2; y^2=x^3+A26(v)x^2+B26(v)x), specialization v=-215/883, minimal model verified via gp elltors (torsion [6,2]). MwRank-based search had failed to resolve this curve. Rank settled rigorously: Magma TwoDescent gives 31 locally-soluble 2-coverings, so the 2-Selmer group has order 32=2^5 and rank(E)<=3 (E[2](Q) has order 4); gp ellrank independently returns [3,3]. Hence rank is exactly 3. The 3 independent points below were found by our 4-descent pipeline (Magma FourDescent covering equations, p-adic PointSearch4Descent on the reduced quadric intersection, mapped back and verified on-curve) and cross-checked with ellrank's small generators; independence certified by canonical-height Gram determinant (regulator 27.73). Self-discovered specialization, not a literature curve.