curve #5763

y² = x³ − 961546199188545041212260747

a-invariants: [0, 0, 0, 0, -961546199188545041212260747]
c-invariants: [0, 830775916098902915607393285408]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 1282061598918060054949680996
discriminant (Δ): -399414712251140842955664058350581264919839659605743139888
Faltings height: 9.5397
naive height: 137.7843
primes of bad reduction: 2, 3, 23, 29, 31, 47, 101, 163, 373
regulator: 12900577074421.1806299016718455196531400877167368453086
submitted by: Maksym Voznyy
submitted at: 2026-10-24 20:07:54 UTC
last updated: 2026-10-24 20:07:54 UTC

(27280624692576806789854447509961171657745715762667/10417772727944558333077950862523005982409, -138621656852279251985126727148162070151273909429566856177931867600571948200/1063315924604210655206368429381289299905405040014648866359173)
(9668843870745125714627201608985610351/2246022622101680123606130625, -29883308809925823685702764624709347602153405256500750526/106444000733295833849972799604335943390625)
(40678210418229261135284765771386807416038907721/25177085481677690453104059278119290000, 7208690922940426799453425312869303856400918917163583053011493877036731/126330490288383244355557801831075842568053862450467000000)
(324822718566947008941515618311362021188457/13444909668941723323624573049764, 185120616527295966047691568279136941471672172443290446748596565/49298855053166480835391071843740313224194098088)
(19540438263555653800926102746545103668766443/96931873655350403712351359555961, 86377658001697626427353923389314526142110744269540653583382972660/954332933489277111502534717995274656353740037709)
(635379084188351279846128520391/84270366550466670025, 505896515529049810858660695264720034209434814/773592631568836733893461381125)
(170352651237134524533213722803968951/87075304189817041768980025, 65641539226233101898223676304201906225486825743531574/812535791656827054882024072472612806125)
(22232255266961610561525486391492081/2727344476817064692640000, 3311993417429413369332902004097670508682790371142729/4504120412394979380527690910912000000)

Voznyy (2023), A = 11935295922962, [r, s, t] = [186, 207, 232] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 20:07:54 UTC · history