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curve #3509

y² = x³ + x² + 805197631x + 22276574524831

a-invariants: [0, 1, 0, 805197631, 22276574524831]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 36476637438549952
discriminant (Δ): -247783851311154249210600226816
Faltings height: 4.3227
naive height: 74.9922
primes of bad reduction: 2, 7, 23, 31, 41, 193, 233, 241, 257
regulator: 47075.8885651117616252156231056657495257178489578090742
submitted by: Michael Rubinstein
submitted at: 2026-09-27 12:46:20 UTC
last updated: 2026-09-27 12:46:20 UTC

Witness: 8 independent points log in to add more points →

(-3237, 4431280)
(2011, 4889168)
(-72365/9, 105550928/27)
(30538, 8680175)
(1380835/121, 7640412976/1331)
(3771, 5036528)
(13029739/529, 91901526416/12167)
(-16371/4, 34790861/8)

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 12:46:20 UTC · history

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