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1 edit.

hdeping · 2026-10-21 12:16:38 UTC

fiber of the x1092 K3 fibration family (file 167_x1092_t0_0085.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -9/19. A(u) = (-1383436870888675706200107)+(-5515600836340711948476888)*u^1+(716527474181252185372992)*u^2+(19599652286308507036273344)*u^3+(-10348738112891504390620680)*u^4+(11954627818857380106162864)*u^5+(-12819504668705779187131920)*u^6+(-9282889399122096275139840)*u^7+(-1414273781478875646923712)*u^8 ; B(u) = (623151887106655251853879329773846694)+(3757259803598750736604123706461347144)*u^1+(3844429892270677596667121714023090128)*u^2+(-16349006985383236996062158267218060800)*u^3+(-30783616351291087563896953575812615016)*u^4+(27168228250111848663166931761100037840)*u^5+(103348463813083983014377415708098752432)*u^6+(-94509325719259964077509140015970425664)*u^7+(-43457863230894151560075098944198688496)*u^8+(25171285331836505034229860335000995200)*u^9+(23456140237510943194372729657306631040)*u^10+(6556407886828091399912763281517445632)*u^11+(637439003051955708260756861597134080)*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.