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curve #3465

y² = x³ + x² − 541973089x + 4299659003007

a-invariants: [0, 1, 0, -541973089, 4299659003007]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 36476637438549952
discriminant (Δ): 2201483554872909197712883712
Faltings height: 3.9762
naive height: 71.9458
primes of bad reduction: 2, 7, 23, 31, 41, 193, 233, 241, 257
regulator: 47075.8885651117616252156231056657495257178489578090742
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:42:37 UTC
last updated: 2026-09-27 05:42:37 UTC

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

(-5411, 2659676)
(-1877, 2304416)
(17002, 7471)
(6493, 1026844)
(20617, 1374664)
(17243, 285344)
(155653/9, -8524628/27)
(17469, -403956)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:42:37 UTC · history

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