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curve #1353

y² = x³ − x² − 1883348105x + 31457608167561

a-invariants: [0, -1, 0, -1883348105, 31457608167561]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 91109902081901376
discriminant (Δ): 53119393665174332399849472
Faltings height: 3.9878
naive height: 75.6826
primes of bad reduction: 2, 3, 17, 89, 223, 257, 3617
regulator: 44460.1003771370253970126109200807666321375801824059992
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:37:19 UTC
last updated: 2026-09-24 17:37:19 UTC

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

(-2017, 5937012)
(24861, 29904)
(24771, 64224)
(-5111, 6399208)
(26819, 487008)
(24605, 115056)
(32799, 2229108)
(29008, 1110763)

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 17:37:19 UTC · history

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