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curve #1650

y² = x³ − x² − 3334327169x + 73887100179585

a-invariants: [0, -1, 0, -3334327169, 73887100179585]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 319218478656
discriminant (Δ): 14142994751545451231323226112
Faltings height: 4.2647
naive height: 77.3962
primes of bad reduction: 2, 3, 7, 11, 17, 73, 127, 137
regulator: 397.596760161882866332682515133115711825630081543
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:25:22 UTC
last updated: 2026-09-25 02:25:22 UTC

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

(67, 8582756)
(36481, 892976)
(38465, 1594320)
(6280121/121, 8485044624/1331)
(2447, 8108184)

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 02:25:22 UTC · history

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