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curve #1277

y² = x³ − 88808223x + 120840818722

a-invariants: [0, 0, 0, -88808223, 120840818722]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 31345170120
discriminant (Δ): 38518701920947646887737600
Faltings height: 3.6024
naive height: 66.5196
primes of bad reduction: 2, 3, 5, 11, 31, 37, 67, 103
regulator: 80.0633469534052244821786354443709065326752315626
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:24:18 UTC
last updated: 2026-09-24 17:24:18 UTC

Witness: 5 independent points log in to add more points →

(76169, 20863062)
(-11431/4, 4741605/8)
(123553/9, 32945374/27)
(-305731/49, -225455670/343)
(-3811, 635562)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:24:18 UTC · history

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