Elliptic Curve Rank Leaderboard
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← curve #5330
Commentary history
1 edit.
hdeping
·
2026-10-21 13:23:52 UTC
fiber 089 of the x1152 K3 fibration, E(u): y^2 = x^3 + A(u)*x + B(u), specialized at T = u = -68/89. A(u) = (-22234134433116285910092921277275)+(110922098753374475218610657758560)*u^1+(-2238835299613016412598155663300)*u^2+(-668291528103291204503696355619440)*u^3+(-1228382975540396813143327213163490)*u^4+(-1305046090974099330756097785833760)*u^5+(-730165036282222351438425309089220)*u^6+(-115184111329442799000859184518320)*u^7+(-6764206525058961744342207836427)*u^8 ; B(u) = (43437345573952011026007762008660031135091893750)+(-272653378639351264146660169730601346460528493600)*u^1+(274681422677639502079180012059258901947525880524)*u^2+(834095500002542547490222678572818893299399330960)*u^3+(-1446190337475684620303144196583106816058012416310)*u^4+(4817627385439859969516421772920670917055554020640)*u^5+(25741889274749849075903353261318279749128611700520)*u^6+(35618011375130752993917833852707386766033265770656)*u^7+(22305750380707309697813397419957100040991477108250)*u^8+(7478862206043393848507380663800830742000201885120)*u^9+(1781657943811020988023763350544021409036455304940)*u^10+(219381245128735196370337431665053397514385169040)*u^11+(9838320680474420154415220509114637635180818246)*u^12. Rank exactly 23: 23 independent witness points (17 from mod-p Shioda fake 2-descent section lift, 6 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; Bober analytic rank bound 23 (kappa=2.8, GRH), rank is exactly 23.
hdeping ·