curve #4687

y² = x³ − 282673567495490277456900x

a-invariants: [0, 0, 0, -282673567495490277456900, 0]
c-invariants: [13568331239783533317931200, 0]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 4522777079927844439310400
discriminant (Δ): 1445558174371182677517654332499558702553071035930050275197136768576000000
Faltings height: 12.5357
naive height: 173.6093
primes of bad reduction: 2, 3, 5, 11, 17, 107, 463, 1913
regulator: 6236366.7268149470601780030078695425944047575476928
submitted by: dujella
submitted at: 2026-10-20 20:39:42 UTC
last updated: 2026-10-20 20:39:42 UTC

(-317205078080, 240309412570889200)
(1110744023070, 1027815645288207600)
(-8842721250, 49989119984694000)
(2350922039070, 3511212519485048400)
(7424745951989070/361, 639554031769152257946000/6859)
(-165395800834700271/51351556, 11103259191546833925683935833/367985250296)

Dujella - Janfada - Salami (2009)

last edited by dujella at 2026-10-20 20:39:42 UTC · history