curve #2182

y² + xy = x³ − 97786754135136291205325201456018300x + 6192618544071258703787593919472934977414964438890000

a-invariants: [1, 0, 0, -97786754135136291205325201456018300, 6192618544071258703787593919472934977414964438890000]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 325662549659052936330
discriminant (Δ): 43277361908658275888523345412176539504875801138769112216765897641050488977184904087439362560000000000000000
Faltings height: 19.1586
naive height: 253.3179
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 79, 101, 223, 313, 49801
regulator: 41899.606156121155751078667372661797846029549
submitted by: Tom Fisher
submitted at: 2026-09-26 17:14:28 UTC
last updated: 2026-09-26 17:14:28 UTC

(274887906914724556, -9147492786135424992704588)
(62718943759824249209034178076092600/1241034587031947761, -51354834432149065162729129239810440358544450486369700/1382534023431602612057272759)
(30248369105401958555069911173485380/89681232159126001, 2890206598473212141332130140412636902647519116897480/26856681562855952889842249)

Found by Flores - Jones - Rollick - Weigandt - Rathbun (2007)

last edited by Tom Fisher at 2026-09-26 17:14:28 UTC · history