curve #5755

y² = x³ − 133260592734439360689126236427

a-invariants: [0, 0, 0, 0, -133260592734439360689126236427]
c-invariants: [0, 115137152122555607635405068272928]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 177680790312585814252168315236
discriminant (Δ): -7671622568803536611435106954574267541656172570321928745774128
Faltings height: 10.3616
naive height: 147.6474
primes of bad reduction: 2, 3, 7, 13, 31, 37, 97, 157, 193, 229
regulator: 408020055659.674685888170359864796338160862396885172312
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:26:04 UTC
last updated: 2026-10-24 19:26:04 UTC

(57444557741687941113/11233032196, 26019982832006749598043148755/1190544150325256)
(4434259160615209/476100, -269829699233272936445323/328509000)
(364079326052555481/26419600, 214015550821663405163057379/135796744000)
(45056015360334158671/3656016225, 291467908635699478184584642594/221061021044625)
(39528320538480911464143922889314287/8217548064689762900929, -7858914133169376757815707540597776090156366702355970/744926423348913005611134486704033)
(612345746093285987024582626833/119171497420927860736, 63812630312904708447347195987727203895963015/1300943976439682828061183574016)
(58951792667011107755739/3099729966025, 14174168514730118986525217192448612/5457400076833445125)
(6609638263359742698825999847609/1168200109734727400100, 8735500357496273887303105483485762303619190477/39927844367434936963845120249000)

Voznyy (2023), A = -140507330893202, [r, s, t] = [207, 322, 418] for S3 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:26:04 UTC · history