curve #5625

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y² = x³ − 46518496784031941912630776032993132

a-invariants: [0, 0, 0, 0, -46518496784031941912630776032993132]
c-invariants: [0, 40191981221403597812512990492506066048]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 46518496784031941912630776032993132
discriminant (Δ): -934835274595867732780023423947324054794311938523612378563745447961191168
Faltings height: 12.4888
naive height: 173.1735
primes of bad reduction: 2, 3, 7, 17, 19, 73, 211, 409, 439, 3319
regulator: 237716993350896.319153253209097285591136386192201431479
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:51:50 UTC
last updated: 2026-10-23 23:51:50 UTC

Witness: 8 independent points log in to add more points →

(291276099934019060919782099768036393171575170824317/805546564349324095180169967087621144369, 629342212410025476771147776041799106568604682717765318348042717742941610795/22863145205546167968074081008658244312504644273583802362153)
(2178113038446556759613049445100740335583754113/4607771248510538173518317132227716, 76042362180246485017295383472528442386507099356580727936320938619455/312778120619968644050031385374757180359120924473736)
(34962961434628686896706412170760208533/20253799618300073198880081, -205797305842858939128666530792715434802400910334222849665/91150648626579475150426704373784880729)
(838351927138496683687010839590366886751815268203091461/137283679077365967869184083498679125625, -767608102858171464581895664583137728883778394543810523575586231482896711626793209/1608527032840159211495254799999480762830906300596326578125)
(270755138288975508109/183467025, 4422819780430175286271290449773/2485060853625)
(345547918413445988796172210741597/91650468662274966129, -6420574098774663803859427131386010036520074151835/877408899592749237722442523383)
(437542356406437867646735558081710597252077217105841/706711094811210373903196525577944001600, 8206423152933206748193286430293116113975442282430562044546660458863683033111/18787234844398460926502233953235003499167860242173359936000)
(1880662144048866176276515530373206743101300609693/289677292651463763112115360177839401, 2578868853296439303339921313635920128171394074422084952485694527922388245/155909177100599466132542865442311930076157297560105899)

Commentary

Voznyy (2023), A = -83015836761366908, [r, s, t] = [22, 39, 189] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:51:50 UTC · history