curve #5761

y² = x³ − 138972845740990854613333913292

a-invariants: [0, 0, 0, 0, -138972845740990854613333913292]
c-invariants: [0, 120072538720216098385920501084288]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 11256800505020259223680046976652
discriminant (Δ): -8343411200646871644688416919607837484423598433793944087778048
Faltings height: 10.3686
naive height: 147.7313
primes of bad reduction: 2, 3, 7, 11, 17, 23, 31, 61, 71, 79, 337
regulator: 14839477825308.1468127087988195148157676863963041207365
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:56:58 UTC
last updated: 2026-10-24 19:56:58 UTC

(9288448010531284325472558288613/9249747225540204681, -28308359489407613389486484751043117010595069305/28131623535248003472312977829)
(984504200092158817/172975104, 484745066404011666321236335/2274968567808)
(72000468222799375075908023295028075741/13502032328848255695657441225, 176565908366010445530095307086393660087280434613736427461/1568912471454599733724529704677514624357125)
(6068066921816604541/931775625, 10536112026301402821124201589/28442450953125)
(979058341776420143637735142753/333345153888576036, 968752545958441242448946287300852427933816815/192460326721756127764434216)
(4938350139789646582888745413/500468228134959681, 320955732257517614095987765518357545671975/354050137777479926600704671)
(474466847325441283317156447459481697209/89578101768125160350295075600, 2630265459312237501545462612013113691352861148184596617427/26810368467446061410391150472591286691096000)
(5784041944275758356668038749773885889/1110217471900166374065345600, 1825002471779508654178068540703615640354340900381413537/36992364061843644299149760265777079104000)

Voznyy (2023), A = 3874153757922756, [r, s, t] = [17, 44, 244] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:56:58 UTC · history