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curve #259

y² + xy = x³ − x² − 27019x + 779689

a-invariants: [1, -1, 0, -27019, 779689]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 502155474290006
discriminant (Δ): 1004310948580012
Faltings height: 1.5733
naive height: 42.2265
primes of bad reduction: 2, 251077737145003
regulator: 7901.93565589253799047372371659535314956067892785832971
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 log in to add more points →

(-176, 333)
(-175, 442)
(-170, 747)
(-164, 965)
(-153, 1223)
(-147, 1322)
(-140, 1413)
(-138, 1435)

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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