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curve #1350

y² = x³ + x² − 569568665x + 5112667264039

a-invariants: [0, 1, 0, -569568665, 5112667264039]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 65155172589047744
discriminant (Δ): 532420327846451128150986752
Faltings height: 3.9100
naive height: 72.0948
primes of bad reduction: 2, 7, 31, 41, 113, 127, 1721
regulator: 19603.1175130692059043909460113256836237182950893251100
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:36:48 UTC
last updated: 2026-09-24 17:36:48 UTC

Witness: 8 independent points log in to add more points →

(-13259, 3214624)
(29455, -3727192)
(-305, 2299208)
(-5385, 2832608)
(-22430/9, -68925059/27)
(-21621, 2705672)
(5029, -1541272)
(16001, -309876)

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 17:36:48 UTC · history

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