curve #4155

y² + xy + y = x³ − 539229717746843020x + 107264396445831660595280070

a-invariants: [1, 0, 1, -539229717746843020, 107264396445831660595280070]
c-invariants: [25883026451848464937, -92676438568023094432094678101]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 13540616083359048987372131941710748131554890287295966
discriminant (Δ): 5064190415176284321277177346199819801201528967448691284
Faltings height: 9.2028
naive height: 134.1004
primes of bad reduction: 2, 11, 17, 2699, 47797, 404017, 694646192655632801382996797032271659
regulator: 906373662493014.6130733818726548152804051282713534737928744019620917220
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 17:18:18 UTC
last updated: 2026-10-11 17:18:18 UTC

(171982674, 4428586285158)
(600510378, -55365218698)
(616750563, 3048382970109)
(816701435, 14546604305919)
(-428389921, -16113374590167)
(3108121660, -168693682708230)
(-611307558, 14438305532559)
(169743045, -4541522734791)
(160163035, 5000746064895)
(-330996771, 15795229986437)
(-524081377, 15682091735799)
(-736019771, 10268169306937)
(6551203075/9, 270584184836965/27)
(2355384157, -109108706370587)
(-20004226994/25, 642489719308214/125)
(13833619303/9, -1456489962971357/27)

Mestre construction: sextuple [-291, -162, -97, -42, 259, 333], T = 4; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x).

last edited by Andrii Prokhorenkov at 2026-10-11 17:18:18 UTC · history