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curve #1644

y² = x³ − x² − 2579998209x + 50413251938049

a-invariants: [0, -1, 0, -2579998209, 50413251938049]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 144443213376
discriminant (Δ): 1213678736535182390340747264
Faltings height: 4.1378
naive height: 76.6268
primes of bad reduction: 2, 3, 7, 11, 23, 31, 71, 193
regulator: 252.111910389332015148075905604337522259004059594
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:17:20 UTC
last updated: 2026-09-25 02:17:20 UTC

Witness: 5 independent points log in to add more points →

(-2911, 7609136)
(32739, 1018164)
(5583, 6015240)
(2979, 6538644)
(2481201/49, 2415769488/343)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:17:20 UTC · history

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