curve #2755

y² + xy = x³ − 750317650367394301235970310370497308826620x + 250157454864721027465417103055839870833708995946817266393040400

a-invariants: [1, 0, 0, -750317650367394301235970310370497308826620, 250157454864721027465417103055839870833708995946817266393040400]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/10ℤ
conductor (N): 37726797710029395854920110
discriminant (Δ): 299810644116431135158796387460597176797913458594578789910447065814296661252883455825323036327972851063131309952190000000000
Faltings height: 22.6856
naive height: 300.8775
primes of bad reduction: 2, 3, 5, 7, 11, 19, 41, 101, 113, 149, 541, 887, 4391, 5851
regulator: 16415492.79722560201353591284197609953813316236
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:20:54 UTC
last updated: 2026-09-26 20:20:54 UTC

(17760263894000822086514356290/37442161, 226532742271018774631384862712751240571120/229108583159)
(350567486458718720405225319497034217440/669960651643360081, 495290473212199696701820612009068834520669710828639069180/548370324397775349309170521)
(1530451596008647220909458187462668626068160/3066234367489948068241, 1057420170110265567532271510484889764084769939474810832791140/169788401885295860993826984340039)
(280334710629211670592640053482279953405109861696485836461666884152120257341860/501817799873780422540987267295127211834713308129625628849, 25975410418297962202363841869199655415723075473006962560844935953987170356511143908042793632875561734493663048342760/11241366131686945263495520264586685947493477023144222601543788490144017129564436177257)

Fisher (2016). Source: https://dujella.github.io/tors/z10.html (curve entry 11). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:20:55 UTC · history