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curve #3464

y² + xy + y = x³ − x² − 374703419x + 2783803557547

a-invariants: [1, -1, 1, -374703419, 2783803557547]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 8217534692466
discriminant (Δ): 19413051300045291298189824
Faltings height: 3.7169
naive height: 70.8385
primes of bad reduction: 2, 3, 11, 41, 71, 727, 2179
regulator: 840.02902024058327162999416256004211796126956375257
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:42:27 UTC
last updated: 2026-09-27 05:42:27 UTC

Witness: 6 independent points log in to add more points →

(9659, 251338)
(10561, 61016)
(12365, -208682)
(-791, 1755302)
(10427, 96458)
(1339, -1512118)

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 05:42:27 UTC · history

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