curve #4562

y² = x³ − x² − 57899x + 28316619

a-invariants: [0, -1, 0, -57899, 28316619]
c-invariants: [2779168, -24448883840]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 961357024128
discriminant (Δ): -333496674384051456
Faltings height: 2.0437
naive height: 47.8397
primes of bad reduction: 2, 3, 17, 19, 43, 53, 179
regulator: 755.63107465434163945257524006293476543242014012058
submitted by: The Wren
submitted at: 2026-10-18 01:59:11 UTC
last updated: 2026-10-18 01:59:11 UTC

Witness: 6 independent points log in to add more points →

(279, 5814)
(602, 14535)
(41, 5100)
(-265, 4998)
(241, 5320)
(58, 5015)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, torsion/torsion_Z2.tsv.gz: https://github.com/mrubinst/elliptic-curves-by-rank. Six supplied rational points checked exactly and certified independent modulo torsion. Rational torsion C2. Source-attributed existing curve.

last edited by The Wren at 2026-10-18 01:59:11 UTC · history