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curve #4054

y² + xy = x³ − 121432822799117x + 515184421561366165009

a-invariants: [1, 0, 0, -121432822799117, 515184421561366165009]
c-invariants: [5828775494357617, -445119348972183608104201]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 192512138106375249526
discriminant (Δ): -58321994207022468188844565065979892432896
Faltings height: 6.8012
naive height: 108.9053
primes of bad reduction: 2, 7, 13, 19, 31, 43, 59, 102013, 6938977
regulator: 71324.7829164536565888566116441737590872890134681952336
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:25:14 UTC
last updated: 2026-10-07 22:25:14 UTC

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(6432898, 473008895)
(-12573446, -7359716649)
(-7348086, 31795622735)
(6675074, 1421458175)
(7805458, 6545488847)
(7181614, 3670191851)
(161271082, -2043442632633)
(3662494, -10936438245)

Commentary

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

last edited by Michael Rubinstein at 2026-10-07 22:25:14 UTC · history

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