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curve #1688

y² + xy = x³ − 3278161153320025x + 208215349960063114525625

a-invariants: [1, 0, 0, -3278161153320025, 208215349960063114525625]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 6907929947418630 ☆ record for ℤ/5ℤ torsion, rank ≥ 6
discriminant (Δ): -16474161943622799392992699237479776821939862400000
Faltings height: 8.1289
naive height: 120.9089
primes of bad reduction: 2, 3, 5, 13, 17, 29, 31, 1158976699
regulator: 2935.2501543659818760441852405834637525475279755215
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:18 UTC
last updated: 2026-09-25 06:10:18 UTC

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

(552017132, 12907507819841)
(1180240130, -40502126801125)
(108749000, -1066741675525)
(12652275245/16, 1419697216534625/64)
(101605430, 961238247695)
(466149350, 9998373160475)

Commentary

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:10:18 UTC · history

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