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1 edit.

hdeping · 2026-10-21 08:08:27 UTC

fiber 133 of the x1152 K3 fibration, E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -27/98. A(u) = (-98446928369392297987858107)+(753656616847155064495894056)*u^1+(-1304662621155467165949437316)*u^2+(-4515151930070151665108601288)*u^3+(-4977701063274588505383095730)*u^4+(-3216158287288357141650052008)*u^5+(-379643944497665001753404196)*u^6+(387597384378623366437498056)*u^7+(-52947472367727871375145067)*u^8 ; B(u) = (455529334666944868668501131133770300694)+(-4406091141778868895239142866363000327928)*u^1+(8711059880694673976260419900526416998364)*u^2+(-3793179221642104157592128359195176701880)*u^3+(24216919834250864412914656434287671696410)*u^4+(200113292396607048670446102942302942345616)*u^5+(266455804027297683905238442306815065604168)*u^6+(107441306099609449962047233442503188641616)*u^7+(-2582417909382033421927144160479025688150)*u^8+(428474205328592695582331592965376042600)*u^9+(2199423551161536880161124686788281724316)*u^10+(-1449946611991997592459259221798535014552)*u^11+(194470684143269906473287684559611258726)*u^12. Rank 22 (exactly): 22 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 5 more from kappa(z*)-covers of the 20 shallowest 2*Lambda_17 coset classes, ratpoints H=1e6, exact halving), 22x22 canonical height det = 6.54e22 != 0; Bober analytic rank bound 22 (kappa=2.8, GRH), root number +1.