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curve #1602

y² + xy + y = x³ − x² − 878103212x + 9994158602799

a-invariants: [1, -1, 1, -878103212, 9994158602799]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 912967290
discriminant (Δ): 185142362968522259100000000
Faltings height: 3.9181
naive height: 73.3934
primes of bad reduction: 2, 3, 5, 19, 23, 139, 167
regulator: 20.34026524089422894190746455272265572079768067
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:25:30 UTC
last updated: 2026-09-25 01:25:30 UTC

Witness: 4 independent points log in to add more points →

(22667, 1306221)
(26657, 2337921)
(-931, 3288453)
(-16093, 4475421)

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 01:25:30 UTC · history

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