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curve #260

y² + xy = x³ − x² − 27589x + 1109929

a-invariants: [1, -1, 0, -27589, 1109929]
rank (lower bound): ≥ 8
conductor (N): 409193376769886
naive height: 42.2891
Faltings height: 1.5628
discriminant (Δ): 818386753539772
primes of bad reduction: 2, 204596688384943
regulator: 28129.6096211469977749715835979105044747370720394565244
submitted by: David Renshaw
submitted at: 2026-07-29 13:42:41 UTC
last updated: 2026-07-29 13:42:41 UTC

Witness: 8 independent points

(-183, 163)
(-177, 740)
(-171, 983)
(-168, 1075)
(-164, 1179)
(-160, 1267)
(-148, 1465)
(-142, 1537)

Commentary

From a dataset compiled by Xiaoyu Huang.

last edited by David Renshaw at 2026-07-29 13:46:57 UTC · history

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