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curve #3462

y² = x³ + x² − 9421065891357x + 11092061421425521756

a-invariants: [0, 1, 0, -9421065891357, 11092061421425521756]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 137823647696020728596
discriminant (Δ): 364919715538550731980291339444458433104
Faltings height: 6.2567
naive height: 101.2355
primes of bad reduction: 2, 7, 11, 31, 53, 59, 109, 1579, 26820991
regulator: 132902.731136926483523201229805555685564399872378495719
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:42:06 UTC
last updated: 2026-09-27 05:42:06 UTC

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

(1641967, 223202133)
(1870503, 120058939)
(1982043, 453379069)
(1929651, 312815699)
(1685745, 31498271)
(-546933, 4010130467)
(7327185, 18315061919)
(1650465, -197100449)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:42:06 UTC · history

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