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curve #1364

y² = x³ − x² − 13744251860x + 403645611431076

a-invariants: [0, -1, 0, -13744251860, 403645611431076]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1115505417782881151832
discriminant (Δ): 95782362706698166453318160838912
Faltings height: 4.8393
naive height: 81.6453
primes of bad reduction: 2, 3, 13, 19, 23, 29, 61, 89, 180241, 288313
regulator: 201614.26245128810785258806772940416446727977535860164067
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:39:11 UTC
last updated: 2026-09-24 17:39:11 UTC

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(-127984, 8142966)
(8958, 16770312)
(21536, 10846074)
(98788, 3153982)
(5669, 18053022)
(17356, 13050986)
(-102530, -27110824)
(-107054, -25458056)
(269134, 127274272)

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 17:39:11 UTC · history

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