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curve #770

y² + y = x³ − 135109x + 18252072

a-invariants: [0, 0, 1, -135109, 18252072]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 323954505704623
discriminant (Δ): 13930043745298789
Faltings height: 1.8558
naive height: 47.0551
primes of bad reduction: 43, 727, 79201, 130843
regulator: 6362.52244218102147563048008904859401132000684898770158
submitted by: Michael Rubinstein
submitted at: 2026-09-18 12:21:21 UTC
last updated: 2026-09-18 12:21:21 UTC

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

(173, 236)
(130, 1698)
(-343, 4923)
(-128, 5783)
(259, 795)
(603, 12491)
(388, -4924)
(168, -544)

Commentary

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

last edited by Michael Rubinstein at 2026-09-18 12:21:21 UTC · history

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