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curve #1336

y² + xy = x³ − 2035462515005x + 1117701559690439025

a-invariants: [1, 0, 0, -2035462515005, 1117701559690439025]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 18666601961882610
discriminant (Δ): 41889034181806847365854852072000000
Faltings height: 5.7201
naive height: 96.6388
primes of bad reduction: 2, 3, 5, 23, 29, 31, 14407, 2088733
regulator: 3665.022022981220090902005170626073440743818928736394
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:34:21 UTC
last updated: 2026-09-24 17:34:21 UTC

Witness: 7 independent points log in to add more points →

(-1568090, -672791705)
(611086, 319154107)
(1479520, -1160409305)
(819190, -3030905)
(58810, -999128705)
(817810, 6090895)
(10955965/16, 13552641955/64)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:34:21 UTC · history

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