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curve #24

y² = x³ − x² − 2388994756x + 44907381038500

a-invariants: [0, -1, 0, -2388994756, 44907381038500]
rank (lower bound): ≥ 6
conductor (N): 405947076034620120
naive height: 76.3960
Faltings height: 4.1330
discriminant (Δ): 1449022372170745950888710400
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 53, 997, 8609
regulator: 2040.2613090018833134080325418276186635913655423722
submitted by: David Renshaw
last updated: 2026-07-01 23:00:16

Witness: 6 independent points

(27448, 112350)
(29750, 405600)
(-14000, 8695350)
(-41724, 8482162)
(117368608, 1271533747770)
(-16300964/289, 2216801226/4913)

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 22:31:56 · history

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