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curve #1356

y² + xy + y = x³ − 270178372266703x + 1711728668715982411506

a-invariants: [1, 0, 1, -270178372266703, 1711728668715982411506]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 18634368691081768030
discriminant (Δ): -3556237867662447616318234077025105468750000
Faltings height: 7.0616
naive height: 111.3067
primes of bad reduction: 2, 5, 7, 37, 59, 79, 103, 109, 367, 491
regulator: 175336.693154936057489668009485700817138591305175743545
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:37:50 UTC
last updated: 2026-09-24 17:37:50 UTC

Witness: 8 independent points log in to add more points →

(10371555, 5016590372)
(7474655, 10477246872)
(-19868330/9, -1294116481456/27)
(2044195, 34174605732)
(758873945/64, 6774777910839/512)
(84493720/9, 44239841419/27)
(-8659605, 58330941572)
(134938255, -1556426994128)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:37:50 UTC · history

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