curve #3059

y² + xy + y = x³ − 255425110305106802414698911353x + 49687082457794764104885126714843336579491148

a-invariants: [1, 0, 1, -255425110305106802414698911353, 49687082457794764104885126714843336579491148]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 1373748530431186186949942270
discriminant (Δ): 7556631150594505898067847544936885651835411200029587028163854110570015401488250000
Faltings height: 15.3438
naive height: 214.7518
primes of bad reduction: 2, 5, 7, 11, 13, 17, 19, 23, 41, 47, 61, 73, 101, 389, 1031, 53147
regulator: 2508393.73042159033948091359184731093824264158992228238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:35:21 UTC
last updated: 2026-09-26 20:35:21 UTC

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

(290587700315187, 35560151863295610182)
(106766193961999, 4861413895971145034450)
(-264270280028326, -9936399301133425055150)
(291954973618919, 4848036938914499570)
(291809089917774, 354927978591676275)
(174449619894979, 3230671166037168098030)
(209395100444959, 2320240812968672738930)
(291667302317624, 3620764823518895075)

Commentary

Dujella - Peral (2020). Source: https://dujella.github.io/tors/z6old678.html (curve entry 65). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:35:21 UTC · history