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curve #30

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

a-invariants: [1, -1, 1, -1608154463, 25555312501831]
c-invariants: [77191414209, -22079442640218273]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 9612838979769443646330
discriminant (Δ): -15946546326759934676023910400
Faltings height: 4.1847
naive height: 75.2668
primes of bad reduction: 2, 3, 5, 75217, 1420015714498561
regulator: 254394.10864036720716591387454974845012295985529802681621
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:09 UTC
last updated: 2026-07-01 22:54:25 UTC

Witness: 9 independent points log in to add more 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 UTC · history

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