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curve #1481

y² + xy = x³ − 51555668082x + 498789246037488516

a-invariants: [1, 0, 0, -51555668082, 498789246037488516]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 860458434
discriminant (Δ): -107468819224750854630197648349890167296
Faltings height: 5.9764
naive height: 95.0251
primes of bad reduction: 2, 3, 11, 17, 19, 181, 223
regulator: 91.8407390784931993851140724342193413729150
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:25:19 UTC
last updated: 2026-09-25 00:25:19 UTC

Witness: 2 independent points log in to add more points →

(30177750/49, 286999382622/343)
(-6766290425604/38651089, -170308079529362061138/240293820313)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:25:19 UTC · history

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