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curve #3506

y² = x³ + x² − 7918379009x + 536458061971615

a-invariants: [0, 1, 0, -7918379009, 536458061971615]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 23999337050845260736
discriminant (Δ): -92550077088964775554969835634688
Faltings height: 4.8245
naive height: 81.3552
primes of bad reduction: 2, 73, 79, 89, 97, 809, 1433
regulator: 666010.79078455139706699556725434178836768142054568452799
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:21:15 UTC
last updated: 2026-09-27 12:21:15 UTC

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

(31387, 17856248)
(5499, 22205432)
(123613, 38032708)
(4242538/9, 8604191501/27)
(1183403, 1283921832)
(121277, 36876972)
(-99621, 18347528)
(7696771/25, 20645854744/125)
(2729, -22690728)

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 12:21:15 UTC · history

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