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curve #1565

y² + xy = x³ + 278026876248170x − 845568216554201565148

a-invariants: [1, 0, 0, 278026876248170, -845568216554201565148]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/8ℤ
conductor (N): 1720479810
discriminant (Δ): -1684309570465762737592659358826312666972160000
Faltings height: 7.3666
naive height: 111.3898
primes of bad reduction: 2, 3, 5, 7, 23, 29, 71, 173
regulator: 96.623867553846555292918691774531180317605139
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:09:19 UTC
last updated: 2026-09-25 01:09:19 UTC

Witness: 3 independent points log in to add more points →

(1749252044, 73163266762778)
(3517309196/625, 468006709506794/15625)
(517436444, 11776060498778)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 01:09:19 UTC · history

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