curve #4600

y² + y = x³ + x² − 4369850x + 39234978510

a-invariants: [0, 1, 1, -4369850, 39234978510]
c-invariants: [209752816, -33900279949720]
rank (lower bound): ≥ 11
torsion subgroup: trivial
conductor (N): 659722595274730880503243
discriminant (Δ): -659722595274730880503243
Faltings height: 3.2502
naive height: 62.3089
primes of bad reduction: 659722595274730880503243
regulator: 20999606.6603794169195200605807521643403948008093401390834209
submitted by: The Wren
submitted at: 2026-10-18 22:30:52 UTC
last updated: 2026-10-18 22:30:52 UTC

Witness: 11 independent points log in to add more points →

(-3423, 118733)
(-3116, 150354)
(1020, 189314)
(-3824, 6453)
(202, -195859)
(3944, 288730)
(-1196, -206766)
(10821/4, -1738395/8)
(6023, 481087)
(2547, -211269)
(2360, -205115)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, rank_11.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Eleven supplied rational points checked exactly and certified independent modulo torsion. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 22:30:52 UTC · history