curve #5565

y² = x³ + x² − 109853602575308105741780x + 8481334719940259041932702461070528

a-invariants: [0, 1, 0, -109853602575308105741780, 8481334719940259041932702461070528]
c-invariants: [5272972923614789075605456, -7327873198060021649771543660818568896]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 4770181345220703583080
discriminant (Δ): 53769269261190698752966654739111222809504775477945586236309564100000000
Faltings height: 12.2722
naive height: 170.7739
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 37, 47, 83, 131, 1759, 26641
regulator: 12479758.62387548633784279173883869448079875228006939
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 08:52:28 UTC
last updated: 2026-10-23 08:52:28 UTC

(-249305245574, 142735135354493250)
(-56900627729, 120614458331819790)
(82179075696, 2942007455565360)
(-19395699128246/529, 1358123372695515283650/12167)
(200945007349/4, 444664853565614745/8)
(30583970984974/49, 146760522759232428150/343)
(20545875108391894/66049, 1127214739587418223684670/16974593)

(u,v) = (447525,804602) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 7.

last edited by Daniel Błażewicz at 2026-10-23 08:52:28 UTC · history