curve #6439

y² + xy + y = x³ − x² − 1494118182199216128226580x + 677822329576008798050675069962829047

a-invariants: [1, -1, 1, -1494118182199216128226580, 677822329576008798050675069962829047]
c-invariants: [71717672745562374154875825, -585638492753348871988428229764187355625]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 20538654399359773718019684431014796780239618248995567371030350
discriminant (Δ): 14989581548157772159815331429709134789952947699751962005604788286836000000
Faltings height: 12.8070
naive height: 178.6043
primes of bad reduction: 2, 3, 5, 41, 67, 16615017918019474754697799159499087311604269909797004709
regulator: 5945793315105138557.91710138434503390322409588817338367983935153530728163973169
submitted by: apkorte
submitted at: 2026-11-03 04:54:53 UTC
last updated: 2026-11-03 04:54:53 UTC

(506532266749, -225758408192524675)
(825903211589, -84777853269913795)
(1924526464249, -2220455314264342075)
(3773657817389, 6984143051676023605)
(933472567045, 310651991792015453)
(15143700556333, 58745046944654918045)
(156831070469, 668846383979726365)
(262036617929011/289, -1285941353656932287675/4913)
(589644454889, -42799318626538895)
(-7109514450509/9, -31546772345211712475/27)
(-1391660610911, 248741221022965205)
(336778359949, 461338044792674525)
(514207095289, 213300259708939205)
(288206262318461/25, 4866280253757200941801/125)
(1460145515269, -1268566455742812835)
(555834350749, 138079978292971325)
(3261788649949, -5523348357685233475)
(-1050595041281, 1043044756526650115)
(36083518827889, -216629286398547776395)
(-20681728004651/16, -42903650490521444905/64)

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