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curve #22

y² = x³ − x² − 1664597956x + 26095909440100

a-invariants: [0, -1, 0, -1664597956, 26095909440100]
c-invariants: [79900701904, -22546386352035008]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 284741255186508120
discriminant (Δ): 1016379901231367708305670400
Faltings height: 4.0697
naive height: 75.3122
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 319083769
regulator: 1856.4874679486537029243421496659543977988291008021
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:04 UTC
last updated: 2026-07-01 23:00:16 UTC

Witness: 6 independent points log in to add more points →

(24378, 57200)
(-25000, 7217010)
(37876, 4169262)
(-12534, 6707512)
(162250/9, 37661120/27)
(2382832/9, 3636914050/27)

Commentary

Found by Penney - Pomerance (1974). A curve of rank exactly 6, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:54 UTC · history

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