curve #5616

y² = x³ − 3628146108750460435236941039285592075

a-invariants: [0, 0, 0, 0, -3628146108750460435236941039285592075]
c-invariants: [0, 3134718237960397816044717057942751552800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 14512584435001841740947764157142368300
discriminant (Δ): -5686607888542558603809638601354004730682166974045435630402530503186812030000
Faltings height: 13.2149
naive height: 181.8867
primes of bad reduction: 2, 3, 5, 11, 13, 17, 29, 41, 107, 227, 587, 593
regulator: 59892314772674.0393934706849712901361400038037391561972
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:12:32 UTC
last updated: 2026-10-23 23:12:32 UTC

(2294821800241472936874383845610889562538716917060492649/571616525108962611369835635156153548648704, 3377479348691430947045491893198231083369435914485254073492273702785645951008200907/432172534689903341780973927785864290609793554838028240185028608)
(1131666904516917896003474848303249/387524155587337699984, 35187308622523070994754387401397548745580878131143/7628658393882736882862125468352)
(5648331078828752743445004985184475680924881/77994647036778123196921816036, -13423882538533506146260213157738623042855443959140100942180327879/21781972004853171448880369758011409306405784)
(1978549485199, -2029088118155463782)
(979843990489018739195492403050161/342924741741882016656, 28185637212101282080877292825438978168937050940009/6350358308883173246348081642304)
(2058447141728812156449397869724682850199/611940782318824648142339481, -88829365312908081028718394833637271143575712016498589995718/15137846463636137259931706723913973597629)
(1148904301015739084277796339/673728108050529, 20174307275948074785154999722007051463888/17487470700333028518417)
(3380124036496803905225940775586906971/1095879696289227778111561, 5817535810471827661096735312638761873087627176921278244/1147213690364053091506498766549663941)

Voznyy (2023), A = -733146047675557230, [r, s, t] = [27, 195, 374] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:12:32 UTC · history