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curve #18

y² = x³ − x² − 2069247973x + 36191779888342

a-invariants: [0, -1, 0, -2069247973, 36191779888342]
rank (lower bound): ≥ 6
conductor (N): 21417609338825700
naive height: 75.9650
Faltings height: 4.1063
discriminant (Δ): 1213641447728106672060786000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 127, 10799
regulator: 854.99378511946814432682065976442547356253336901804
submitted by: David Renshaw
last updated: 2026-07-01 23:00:16

Witness: 6 independent points

(28366, 564642)
(41701, 4734687)
(27337, 230775)
(41709/4, 31747841/8)
(85581, 22043153)
(128029/4, 13266729/8)

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 22:31:50 · history

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