Commentary history

1 edit.

hdeping · 2026-10-21 12:16:46 UTC

fiber of the x1092 K3 fibration family (file 157_x1092_t0_0071.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -1/51. A(u) = (-133266803352683433867)+(-34429351041428677740648)*u^1+(-5159465855422129650830724)*u^2+(-199867014403654025300872824)*u^3+(-3674407941552005191068242130)*u^4+(-39203515617102192576477557016)*u^5+(-242832298117300513973865560484)*u^6+(-697681340718393915812184817032)*u^7+(-718622366318760700413751004667)*u^8 ; B(u) = (539316574939092550969221207750)+(261194186737739667071325677113080)*u^1+(52894082157207048461637283455819900)*u^2+(4127823374881053534231122609192191800)*u^3+(235551250432437047361240270551409681450)*u^4+(8604812583907478066799326365826483591280)*u^5+(187613055547997482853550846684987195861000)*u^6+(2452920875396144599562109396854511343838640)*u^7+(19341237044985803273673258128017269067453050)*u^8+(91311139145529018029385201123473804359568280)*u^9+(253761827381667465095652734751449752291673916)*u^10+(383945461130653860983197400998299471308869656)*u^11+(243804338752456642528814405356804610148815574)*u^12. Rank exactly 20: 20 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 3 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 20 (kappa=2.8, GRH), rank is exactly 20.