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curve #3510

y² = x³ + x² − 14648601729x − 343962281385953

a-invariants: [0, 1, 0, -14648601729, -343962281385953]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 59674364161385812544
discriminant (Δ): 150063951290671682034471954317312
Faltings height: 4.8703
naive height: 81.8364
primes of bad reduction: 2, 17, 89, 271, 409, 463, 7937
regulator: 981057.11582122497865572424685978957255833767684453085718
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:46:30 UTC
last updated: 2026-09-27 12:46:30 UTC

Witness: 9 independent points log in to add more points →

(-34117, 10774696)
(-79107, 17883116)
(-343454/9, 340968167/27)
(3819491/25, 3921449464/125)
(289931, 140643640)
(-85381, 16862296)
(1512997/9, 1190603908/27)
(-37798, 12478999)
(240731, 100401320)

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 12:46:30 UTC · history

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