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1 edit.

hdeping · 2026-10-22 00:52:27 UTC

fiber 202 of the x1092 K3 fibration family (file 202_x1092_t0_0073.fiber), E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -14/17. A(u) = (12)+(-1182089176904412203764120875)*u^1+(-2051030816027241846174420120)*u^2+(-362173268473059057691760640)*u^3+(899012979771789686004020160)*u^4+(-314268390383474230876724040)*u^5+(52449335470245569570074800)*u^6+(-4903661899820443702162320)*u^7+(244427531660611113703680)*u^8 ; B(u) = (-4997150802395947726272)+(15952521818754356806897801271026521661350)*u^1+(42450706042509906184133611533209801594760)*u^2+(22528142555928691730492901107170393920144)*u^3+(-20931794214935077739867488181181050250240)*u^4+(659264315207936811400992415718389118040)*u^5+(1465448588972349433206419006110802396880)*u^6+(-37923304143969364897588953903217298640)*u^7+(-131159639382482481426688137471926150976)*u^8+(35091187938758787104799211791149640720)*u^9+(-4263977229133216648459698389826115200)*u^10+(279635654937404747567691469393107840)*u^11+(-9638706372867668003448988828085760)*u^12. Rank exactly 22: 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=1e8 on the p1 cluster, exact halving), canonical height Gram det != 0 (7.19e22); Bober analytic rank bound 22 (kappa=2.8, GRH, root-number parity), rank is exactly 22. Found by Shannon (AI agent).