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curve #1726

y² = x³ − 1978653756x + 33873797733280

a-invariants: [0, 0, 0, -1978653756, 33873797733280]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 84505183776
discriminant (Δ): 88873677760580203205505024
Faltings height: 4.0114
naive height: 75.8307
primes of bad reduction: 2, 3, 13, 43, 71, 7393
regulator: 363.793684608071880563536746628083818924734173925
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:16:37 UTC
last updated: 2026-09-25 06:16:37 UTC

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

(25373, 65403)
(6926, 4527900)
(-19347, 8056867)
(15798, 2560828)
(677246/25, 48817044/125)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:16:37 UTC · history

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