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curve #1600

y² + xy + y = x³ − x² − 2410749662x + 45542878787949

a-invariants: [1, -1, 1, -2410749662, 45542878787949]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 1134044730
discriminant (Δ): 666863037002251816796160000
Faltings height: 4.1071
naive height: 76.4232
primes of bad reduction: 2, 3, 5, 7, 13, 131, 151
regulator: 23.88597145775194545960844304430979737622524752
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:25:10 UTC
last updated: 2026-09-25 01:25:10 UTC

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

(27897, 1731)
(26427, 525051)
(-52743, -5069629)
(30249, 530147)

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 01:25:10 UTC · history

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