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curve #1541

y² + xy = x³ − x² − 225797652x + 1069530106752

a-invariants: [1, -1, 0, -225797652, 1069530106752]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 3091842
discriminant (Δ): 242670371283635049117471888
Faltings height: 3.7803
naive height: 69.3191
primes of bad reduction: 2, 3, 13, 73, 181
regulator: 62.284416091709485540473466887769115782881481
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:52:31 UTC
last updated: 2026-09-25 00:52:31 UTC

Witness: 3 independent points log in to add more points →

(816579/4, 735126525/8)
(-537759/49, 513592596/343)
(1482156/121, 492501744/1331)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:52:31 UTC · history

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