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curve #1328

y² = x³ + x² − 230853065x + 1349233034359

a-invariants: [0, 1, 0, -230853065, 1349233034359]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 42717604222528
discriminant (Δ): 869217211990058961047552
Faltings height: 3.5343
naive height: 69.3855
primes of bad reduction: 2, 17, 47, 89, 263, 401
regulator: 1900.763867305267473880830899780510955691898733220886
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:32:59 UTC
last updated: 2026-09-24 17:32:59 UTC

Witness: 7 independent points log in to add more points →

(237, 1137776)
(-3758, 1470959)
(8227, 83096)
(-109829/9, 41383576/27)
(-2789, 1404064)
(438279/49, 2275552/343)
(14619, 1048288)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:32:59 UTC · history

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