curve #4561

y² = x³ − 99598746x + 382585698565

a-invariants: [0, 0, 0, -99598746, 382585698565]
c-invariants: [4780739808, -330554043560160]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 2019047112
discriminant (Δ): 54642513905165770704
Faltings height: 3.1210
naive height: 66.8636
primes of bad reduction: 2, 3, 31, 43, 109, 193
regulator: 297.4398533132935649415694794501494257681215321
submitted by: The Wren
submitted at: 2026-10-18 01:58:27 UTC
last updated: 2026-10-18 01:58:27 UTC

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

(22913/4, 35217/8)
(6341, 77400)
(5618, 18837)
(16790, 1855665)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z4.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Four supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C4. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 01:58:27 UTC · history