curve #2803

y² + xy + y = x³ − x² − 3957522204786046962200201992567404677x + 3029988614585142118644653464298252623281447852094930301

a-invariants: [1, -1, 1, -3957522204786046962200201992567404677, 3029988614585142118644653464298252623281447852094930301]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/9ℤ
conductor (N): 510544475190063481104630
discriminant (Δ): 770064698830246592747401904618361513963858621857072785912831417187954445444012773377922323910373201000000000
Faltings height: 19.7297
naive height: 264.4196
primes of bad reduction: 2, 3, 5, 7, 11, 29, 37, 109, 181, 1153, 5413, 185869
regulator: 1115993.310753758589174440914213049515002690501
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:23:07 UTC
last updated: 2026-09-26 20:23:07 UTC

Witness: 4 independent points log in to add more points →

(278740355978639028799/324, 2985375750394264421113834704143/5832)
(93410653214501033409/64, 308488186632088692174687589523/512)
(19029226654785323829049791/16982641, 3423877156972834911022891319624984864/69985463561)
(3580024436460833576652855286390352541290023247188591771/9288521204880385620235290175140894121, 35379277977384751025092882844234659759886850651086816874574493227432324517604950656/28308696043763824276611476156575255353520928521305341419)

Commentary

Dujella - Petricevic (2021). Source: https://dujella.github.io/tors/z9.html (curve entry 5). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:23:07 UTC · history