Commentary history

← curve #5289

1 edit.

hdeping · 2026-10-21 12:16:35 UTC

fiber of the x1152 K3 fibration family (file 063_x1152_A_0003.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -4/55. A(u) = (-9585496518629293615819721472)+(-536501816413053749656301196288)*u^1+(-12368010625534698965575586486784)*u^2+(-153670852784977847815038932888064)*u^3+(-1126077980994120736641769318298880)*u^4+(-4916607522934484171617568222893056)*u^5+(-12090799466059737633435362494243584)*u^6+(-14587262243584009021750010492175552)*u^7+(-6844291761509816231381594824587312)*u^8 ; B(u) = (374502094435674025104043654117865569935360)+(33193601381088363486746606727381236442316800)*u^1+(1289004250376379330798378598319831835979161600)*u^2+(28827565230794722135124600956050588624882278400)*u^3+(411108117101856888285966528948531742337079951360)*u^4+(3917967010548910874456925019692368143550867005440)*u^5+(25483742971305896595171553802128442605475798507520)*u^6+(113730906815932001693278266355855041235272854799360)*u^7+(345910796938972022540354749372936686129388052501760)*u^8+(702809951568307885052748475426214338146465682967040)*u^9+(911994372915445045966812634121039331292285376811264)*u^10+(677012143418988419778649816019731910499434169371904)*u^11+(216718499633097826210902038787366269826187097759616)*u^12. Rank exactly 19: 19 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 2 more from kappa(z*)-covers of the 20 shallowest 2*Lambda_17 coset classes, ratpoints H=1e6, exact halving), canonical height Gram det != 0; Bober analytic rank bound 19 (kappa=2.8, GRH), rank is exactly 19.