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curve #1670

y² + xy + y = x³ − 3501861784158x + 2022557744193534556

a-invariants: [1, 0, 1, -3501861784158, 2022557744193534556]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 50250886947030
discriminant (Δ): 981181130155237099516458849261120562500
Faltings height: 6.1970
naive height: 98.2666
primes of bad reduction: 2, 3, 5, 7, 11, 23, 29, 31, 89, 11821
regulator: 277.043009441706956841484410033481652320767339713
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:52:19 UTC
last updated: 2026-09-25 02:52:19 UTC

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

(3165815, 4759228917)
(11478665, 38390249067)
(5844635/4, -1279180989/8)
(258199958/169, 1071482718528/2197)
(-1855999, -1458041121)

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 02:52:19 UTC · history

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