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curve #17

y² = x³ − x² − 832328021x + 9183124281870

a-invariants: [0, -1, 0, -832328021, 9183124281870]
rank (lower bound): ≥ 6
conductor (N): 1064348253719210460
naive height: 73.2328
Faltings height: 3.9492
discriminant (Δ): 474897013203413671310840400
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 2385437629
regulator: 2701.6399282525630330343209741966428056184437506230
submitted by: David Renshaw
last updated: 2026-07-01 23:00:15

Witness: 6 independent points

(15541, 34307)
(9333, 1492605)
(7129, 1900453)
(-186011/9, 113131711/27)
(1637171/49, 1482112071/343)
(1378809, 1618682523)

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 22:31:49 · history

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