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curve #1318

y² + xy + y = x³ − 4587038098x + 173507133935256

a-invariants: [1, 0, 1, -4587038098, 173507133935256]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 21176639504110
discriminant (Δ): -6828307063690267431093394562500
Faltings height: 4.6179
naive height: 79.0976
primes of bad reduction: 2, 5, 59, 67, 107, 139, 181, 199
regulator: 1293.6962665254762687736220427413686637079556858241
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:31:17 UTC
last updated: 2026-09-24 17:31:17 UTC

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

(169795, -65582273)
(-30805, -16883673)
(394765/9, -203894951/27)
(-8360, 14539327)
(360855/4, 177430341/8)
(1060005/49, -3154844139/343)

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 17:31:17 UTC · history

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