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curve #16

y² = x³ − x² − 23308665x + 43082703225

a-invariants: [0, -1, 0, -23308665, 43082703225]
c-invariants: [1118815936, -37216742690816]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 7727548608960
discriminant (Δ): 8906772526687296000000
Faltings height: 3.0487
naive height: 62.5066
primes of bad reduction: 2, 3, 5, 17, 113, 769, 5449
regulator: 419.30996796981054607112068235104029618565968205028
submitted by: David Renshaw
submitted at: 2026-05-27 22:11:59 UTC
last updated: 2026-07-01 22:59:18 UTC

Witness: 6 independent points log in to add more points →

(405, 183600)
(-435, 230520)
(2445, 26520)
(4085, 126560)
(695, 164980)
(3705, 87000)

Commentary

Found by Rignaux (1921). A curve of rank exactly 6, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:48 UTC · history

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