Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #24

y² = x³ − x² − 2388994756x + 44907381038500

a-invariants: [0, -1, 0, -2388994756, 44907381038500]
c-invariants: [114671748304, -38799289186774208]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 405947076034620120
discriminant (Δ): 1449022372170745950888710400
Faltings height: 4.1330
naive height: 76.3960
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 53, 997, 8609
regulator: 2040.2613090018833134080325418276186635913655423722
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:05 UTC
last updated: 2026-07-01 23:00:16 UTC

Witness: 6 independent points log in to add more 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 UTC · history

Log in to edit commentary.