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curve #1642

y² = x³ + x² − 155099889x + 8695417815711

a-invariants: [0, 1, 0, -155099889, 8695417815711]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 100389817248
discriminant (Δ): -32425245055821130033847832576
Faltings height: 4.1504
naive height: 73.1108
primes of bad reduction: 2, 3, 7, 19, 37, 41, 71, 73
regulator: 321.564117277906889804499850638579217401054012923
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:15:19 UTC
last updated: 2026-09-25 02:15:19 UTC

Witness: 5 independent points log in to add more points →

(18621/4, 22732245/8)
(1575, 2907756)
(-3801, 3038100)
(132999, 48380460)
(2583, 2883060)

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 02:15:19 UTC · history

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