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curve #1299

y² = x³ + x² − 1574345x + 756199159

a-invariants: [0, 1, 0, -1574345, 756199159]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 73879116224
discriminant (Δ): 2358680031423598592
Faltings height: 2.3687
naive height: 54.4217
primes of bad reduction: 2, 23, 41, 73, 409
regulator: 302.37721183355163537959023364507987274104888752246
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:28:03 UTC
last updated: 2026-09-24 17:28:03 UTC

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

(-1203, 30176)
(1626, 49979)
(2569, 116932)
(-1433, 8464)
(269, 18768)
(4455, 286672)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:28:03 UTC · history

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