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curve #1559

y² + xy + y = x³ − x² − 25902404062683x + 57038896693004866443

a-invariants: [1, -1, 1, -25902404062683, 57038896693004866443]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/7ℤ
conductor (N): 6514079774
discriminant (Δ): -293239601560074434533783454833010114822144
Faltings height: 6.6860
naive height: 104.5037
primes of bad reduction: 2, 47, 79, 877199
regulator: 1457.3040270361510159173406980710817606520708
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:05:39 UTC
last updated: 2026-09-25 01:05:39 UTC

Witness: 3 independent points log in to add more points →

(1267105219/361, 20977907588542/6859)
(24182866741/17161, 10858385295328788/2248091)
(26968889291/196, 4425715958236315/2744)

Commentary

Torsion Z/7. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:05:39 UTC · history

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