curve #2112

y² + xy = x³ − 626907754382991993084098797339x + 224100727413525092581867026604351108909948625

a-invariants: [1, 0, 0, -626907754382991993084098797339, 224100727413525092581867026604351108909948625]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/4ℤ
conductor (N): 1286799043897115641009631514
discriminant (Δ): -5927011997469733478084159438489975197194794437471806589185498445051084862234765925763826688
Faltings height: 16.1386
naive height: 217.7645
primes of bad reduction: 2, 3, 7, 11, 13, 17, 29, 31, 41, 47, 53, 61, 113, 193, 281, 599, 613
regulator: 103884004.383278508761412488973949128598248526783244151
submitted by: Steps Unbounded
submitted at: 2026-09-26 06:58:19 UTC
last updated: 2026-09-26 06:58:19 UTC

(65200302688250, 13546339832410634138525)
(4000915521078705650/11449, 8460745176281196532031794495/1225043)
(379245961407350, 6394879919991954032585)
(10598218585197566/25, 734454603742419861811021/125)
(-27584220480260773216/75625, -418135151232821809061703578627/20796875)
(-6728212053326945326/113569, -618354255977683313423504866327/38272753)
(-926113083062074, 3220946140893815688353)
(5422927137125150, 395351257878063233872145)

2-isogenous partner of curve#1109 (Dujella - Peral (2016)). Isogenous to curve#2110, curve#2111 (also ours).

last edited by Steps Unbounded at 2026-09-26 21:48:02 UTC · history