curve #3444

y² = x³ + x² − 9909839449x + 379470040610151

a-invariants: [0, 1, 0, -9909839449, 379470040610151]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 23999337050845260736
discriminant (Δ): 76469968516775368507566854144 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
Faltings height: 4.4779 ☆ record for ℤ/2ℤ torsion, rank ≥ 9
naive height: 80.6640
primes of bad reduction: 2, 73, 79, 89, 97, 809, 1433
regulator: 333005.39539227569853349778362717089418384071027284226399
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:34:39 UTC
last updated: 2026-09-27 05:34:39 UTC

(67841, 4405988)
(112555, -26267816)
(58643, 64240)
(4331, 18347528)
(84631, -12122672)
(117611, 28996792)
(52815, -1846104)
(-12757, -22445800)
(39041, 7217188)

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:34:39 UTC · history