curve #1686

y² + y = x³ + x² − 33274691675660x + 73881263922133488464

a-invariants: [0, 1, 1, -33274691675660, 73881263922133488464]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/5ℤ
conductor (N): 4015669710885 ☆ record for ℤ/5ℤ torsion, rank ≥ 5
discriminant (Δ): -165142822338802779031702929865341796875 ☆ record for ℤ/5ℤ torsion, rank ≥ 5
Faltings height: 6.4156
naive height: 105.0211
primes of bad reduction: 3, 5, 7, 19, 43, 46810861
regulator: 526.480825514970530257832329017711001106011406824
submitted by: Michael Rubinstein
submitted at: 2026-09-25 04:48:47 UTC
last updated: 2026-09-25 04:48:47 UTC

(3223561, -339723563)
(-5818064, 8398504687)
(42390001/16, 133030659793/64)
(953404504/289, 547549567856/4913)
(702974239/49, -17318210695484/343)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 04:48:47 UTC · history