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curve #1241

y² = x³ − x² − 4417240x + 3416058256

a-invariants: [0, -1, 0, -4417240, 3416058256]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 778285688496
discriminant (Δ): 479252537115788593152
Faltings height: 2.7268
naive height: 57.5167
primes of bad reduction: 2, 3, 17, 47, 53, 101, 223
regulator: 451.33595530795225753051399313710699449806828391345
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:38:11 UTC
last updated: 2026-09-24 14:38:11 UTC

Witness: 6 independent points log in to add more points →

(-2374, 22746)
(-590, 76266)
(3424, 168588)
(5208, 348772)
(8608, 776628)
(35536, 6687324)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 14:38:11 UTC · history

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