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curve #15

y² = x³ − 856967076x

a-invariants: [0, 0, 0, -856967076, 0]
c-invariants: [41134419648, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 13711473216
discriminant (Δ): 40278416178577537588263358464
Faltings height: 4.1783
naive height: 73.3203
primes of bad reduction: 2, 3, 7, 17, 41
regulator: 172.7920313416794830582707377111743516153900428
submitted by: David Renshaw
submitted at: 2026-05-27 22:11:58 UTC
last updated: 2026-07-01 23:03:10 UTC

Witness: 4 independent points log in to add more points →

(-4998, 2039184)
(34476, 3381300)
(53958, 10528848)
(1843559424/25, 79156334875968/125)

Commentary

Found by Wiman (1945). A curve of rank exactly 4, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:47 UTC · history

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