Commentary history

1 edit.

hdeping · 2026-10-21 12:16:43 UTC

fiber of the x1092 K3 fibration family (file 222_x1092_t3_0357.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -9/34. A(u) = (-176037064306992808566507)+(5915756000685239016284448)*u^1+(-74739832214501898117378864)*u^2+(407193784801308814869840384)*u^3+(-357852151289462141058677280)*u^4+(-6136035049085750455308401664)*u^5+(20390581978882532274482816256)*u^6+(24085910297771228781276198912)*u^7+(-138434852508586604980011424512)*u^8 ; B(u) = (29353282297132394631805644617637606)+(-1465800220984727623268853753715246176)*u^1+(29684854589829915583090967820635629584)*u^2+(-302504492712046802509595254047692878080)*u^3+(1489300822836997474656472031816649171360)*u^4+(-1859111704531363363401367591512810029568)*u^5+(-8901302556884468646838941329449484892672)*u^6+(7835621959513555079061283351216613480448)*u^7+(5887180595638993725830206009454293117440)*u^8+(905676905416813548887689587645787310653440)*u^9+(-2692953602420758530115438575793251800838144)*u^10+(-4969979756041599501329003211795628338610176)*u^11+(18717651081077897840135894513712398618025984)*u^12. Rank exactly 21: 21 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 4 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 21 (kappa=2.8, GRH), rank is exactly 21.