curve #2901

y² = x³ − 636018282314232937750225x

a-invariants: [0, 0, 0, -636018282314232937750225, 0]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 20352585034055454008007200
discriminant (Δ): 16466025088427243524013795733436718809532818356620276045546854930729000000
Faltings height: 12.7384
naive height: 176.0421
primes of bad reduction: 2, 5, 7, 17, 97, 173, 79873
regulator: 206180094.6006557895749314710527906453024507306912545
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:34 UTC
last updated: 2026-09-26 20:27:34 UTC

Witness: 7 independent points log in to add more points →

(2349199039600, 3386809128504045300)
(41883387252225625/50176, 2531093164311743323699875/11239424)
(6509060981758225/1764, 512730950467913482286575/74088)
(-146714976202711/256, 1719681914167176638763/4096)
(-175963973031/1600, 535262302497630295203/64000)
(35159109215008497740224/13053291001, 6296998563844081793621591937052968/1491351550155251)
(2829381632947105879686876/212780569, 4759236582163811059977032999691297174/3103830160003)

Commentary

Watkins et al. (2014), §15 electronic data, rank ≥ 7 congruent-number twist d=797507543735; https://doi.org/10.5802/pmb.9 ; witness x-coordinates: https://magma.maths.usyd.edu.au/~watkins/PTS.r6r7

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:34 UTC · history