curve #5760

y² + y = x³ − 665249617869608439281876280769

a-invariants: [0, 0, 1, 0, -665249617869608439281876280769]
c-invariants: [0, 574775669839341691539541106584200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 215540876189753134327327914969075
discriminant (Δ): -191184647360685142507498399384447853286743014732930014231301875
Faltings height: 10.6296
naive height: 150.8631
primes of bad reduction: 3, 5, 7, 11, 13, 31, 43, 73, 109, 113, 157
regulator: 9922566481037.09179128583561491975409905272355007827990
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:51:50 UTC
last updated: 2026-10-24 19:51:50 UTC

(2503268911588744458152907689951658659929/256301928494421609891160160100, 66976106865364158388875662866393369812880980272165053305967/129756108127755522963856764994368081581151000)
(4295263399705146227157839444025838756471290887089/14410289122717825398178662966488838276, -8901828992179994639564409722392032434077183675691207822878694641456866251/54702735141515308260767121948400626161857715700033593976)
(660675811604341093568569/59497310902500, 385055361534443937959546892594056503/458929532780888625000)
(3813351072026414098771272005270843876815387977374569/7171860241102317475556200923846695088036, 235482817801469846483810764404562238751359941472151715871732034555949033758095/607362154145400903597119255709560925471162347415210771042216)
(3011099386615817096758589209/96682809238696836, 163400045782715707472636191933376623502935/30062416768650604578088584)
(233664661429318674565771407639102049/279375039224762357609604, -112950799028796143563387084032062254502743389271319011/147666303080238103036691013431858808)
(540207834524547994719298010929/61804193651835834276, -24406824395180988188627827014393850144845755/485877644010468259152649637976)
(8447406248125354916588069344006606407961/314959007411773434883383728400, 762896357412055433869428291106103271294890088079176594943709/176758802098230704176202854276634180654952000)

Voznyy (2023), A = -8476258533687945, [r, s, t] = [4, 34, 109] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:51:50 UTC · history