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curve #30

y² + xy + y = x³ − x² − 1608154463x + 25555312501831

a-invariants: [1, -1, 1, -1608154463, 25555312501831]
rank (lower bound): ≥ 9
conductor (N): 9612838979769443646330
naive height: 75.2668
Faltings height: 4.1847
discriminant (Δ): -15946546326759934676023910400
primes of bad reduction: 2, 3, 5, 75217, 1420015714498561
regulator: 254394.10864036720716591387454974845012295985529802681621
submitted by: David Renshaw
last updated: 2026-07-01 22:54:25

Witness: 9 independent points

(23045, 844952)
(34381, 3285026)
(25583, 1062950)
(20803, 1040006)
(21715, 923702)
(17731, 1608326)
(15371, 2106046)
(19507, 1258166)
(18715, 1409582)

Commentary

Found by Brumer - Kramer (1977). A historical rank ≥ 9 record, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:32:02 · history

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