curve #531

y² + xy = x³ − 14434874825407160378486151513293173297576692846882970x + 666295083597084305646805758545896080953899398058757607267876586152607460749412

a-invariants: [1, 0, 0, -14434874825407160378486151513293173297576692846882970, 666295083597084305646805758545896080953899398058757607267876586152607460749412]
rank (lower bound): ≥ 28
torsion subgroup: trivial
conductor (N): 24893914653114600820002303022719951225067845254516373791708191258325404841850345131746902399724935711465272513524024923358435880544090
naive height: 371.9181
Faltings height: 28.7894
discriminant (Δ): 708789221230308448100942156607675064245927269696245962001121787950454558390624080176892670563501007115536579584955185815431835802233925798562789316608000000
primes of bad reduction: 2, 3, 5, 7, 13, 17, 31, 47, 79, 665728186021911859162838946398699868591128696471638326339797624006177280279517057417836409500159691246105797698415864916369
regulator: 6138393186589876708240682981348034.802223199672235728748114712875934605580761286823499025847293
submitted by: Mundoamundo
submitted at: 2026-09-02 17:05:36 UTC
last updated: 2026-09-02 17:05:36 UTC

Witness: 28 independent points log in to add more points →

(96227104159739644834308164, -410242272000043937579265777154583136682)
(2407017552699018336543764, -794710030224575535954575055214695619882)
(720560670638863878009659092, -19088890123629954298789845343226956315370)
(6829536948104231516873991368/169, -847928439435125305108103801005195290658930/2197)
(-146817612541549374426389324/9, -25577865518951080459858363147423029621614/27)
(43949244942077127516985364, -341734968538356818592379346035875447082)
(55577518023945294620396864, -188975576374429728187691061745154902582)
(65941046480951344082533724, -34214253591501772355455367060809110802)
(8915265942257406979587889364, -841709479197919431347660060629479650914282)
(2232897344084375578894428764, 105362623794348908363377151179081270555118)
(-66673019036183516202928636, 1154266331913550223315159997589248650918)
(73354538315648592729168464, -46304227521600010104332476183771284682)
(-118260920638921158902074036, -848187110780153555415200725890088239682)
(57204594148496382602088764, -166578129427904832133075113458484544882)
(75004053641576862345351764, 74594683333807560544219632190879492118)
(76588198217110049007591764, -100007070886879478897293739373324907882)
(110511595822201934076520514, -648638161371869989714568039928984289132)
(62102130663582345600887780896551416564/1244342481001, 367754779006644505947349274227206993015420390505036651918/1388065281899096501)
(2404274328051635586231350961884225427540925324/40383869679667037241, 34363568315660486277575082450268905167863863331894013770672156892998/256632643558047613410046708461)
(11559930633004917254134016805164/160801, 680789661717844625359765036184263801573864318/64481201)
(158596502618393679491912303276/2209, -371186224349288974517295440631091724817686/103823)
(11050581074577025207955665124410802/165199609, -11244547005541239830963605081838913805539864169468/2123310574477)
(1336454208800455609710213620867242379896904/20410556519139361, 125615314846646004396982783737917332457078016784302435188938762/2915964750185678242593359)
(11639474374055067431775356911064/361201, -105145258147171733446813301335866182110067831482/217081801)
(63879070477473874314860547585922496/747639649, 4867692769541566977578513971602321960412164905243306/20442710922607)
(7103573007697732128574035187914093135284/94982742236281, -65765654974628749798437012334457194747402301360940923914978/925693162405251124429)
(50662837238100737379258634024265159/825183076, 2540025855450096674352096348635097534039747098548763/23704209041176)
(-67646004486561052011260636, -1154647044384580506169018956064878314282)

Commentary

Fiber t = -23005/4407 of Elkies' rank-17 elliptic K3 fibration (arXiv:2608.25406). Found by a Mestre-Nagao sieve over t = a/b followed by a 2-covering (fake 2-descent) point search on deep-hole cosets of the rank-17 Mordell-Weil lattice; 17 points are specializations of the generic sections, 11 were found on the coverings. Search run by Claude (Anthropic) with Seth Lupo, 2026-09-02.

last edited by Mundoamundo at 2026-09-02 17:05:36 UTC · history