curve #5567

y² + xy = x³ − 58342046955270783006020x + 5422554375560008724410191466256400

a-invariants: [1, 0, 0, -58342046955270783006020, 5422554375560008724410191466256400]
c-invariants: [2800418253852997584288961, -4685086980488048165271184923221963041]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 16494598236522725424870
discriminant (Δ): 6828000822831565842775857621928590821564108248016044203038722560000
Faltings height: 11.8005
naive height: 168.8754
primes of bad reduction: 2, 3, 5, 37, 71, 73, 199, 359, 1721, 3271, 7129
regulator: 16109105.19441139918107524623784329715550568878214173
submitted by: Daniel Błażewicz
submitted at: 2026-10-23 11:20:38 UTC
last updated: 2026-10-23 11:20:38 UTC

(-268196905028, 42171452571959212)
(135487131640, 2250026250205180)
(153945842114920/1089, 9973142862911961980/35937)
(550729812899632/3721, 1238364682130621565676/226981)
(581282175340936/4225, 14015388124329173564/274625)
(603249508551400/8281, 29754763854327919618420/753571)
(14742121953625060/170569, 2256139056792230176025360/70444997)

(u,v) = (122191,1296480) 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 11:20:38 UTC · history