curve #5617

y² = x³ − 2820599163381463714123577316870075

a-invariants: [0, 0, 0, 0, -2820599163381463714123577316870075]
c-invariants: [0, 2436997677161584649002770801775744800]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 11282396653525854856494309267480300
discriminant (Δ): -3436896804682268030985726400332860963052333031125943790819993978430000
Faltings height: 12.0216
naive height: 167.5677
primes of bad reduction: 2, 3, 5, 7, 13, 17, 41, 59, 67, 83, 137, 239
regulator: 101259374448.787363829240842729586780373615118673905329
submitted by: Maksym Voznyy
submitted at: 2026-10-23 23:23:41 UTC
last updated: 2026-10-23 23:23:41 UTC

(31159672785336023741089/2345464900, 5500334116144989002382378749384687/113590865107000)
(55769379391037715841/57608100, 415831687035945562635749998111/437245479000)
(741152992973689/1156, -20068976446211935010413/39304)
(43422551546632023091/264745441, -171857005561830646425728722636/4307673070511)
(681667965594959641/49284, 562806489277148719973701661/10941048)
(103230884284369/324, 1002076338360082668103/5832)
(24213669483019/121, -95914828268817394472/1331)
(139863909538279449121/3920400, 1654087508880257788632154965169/7762392000)

Voznyy (2023), A = 20441784235315170, [r, s, t] = [369, 378, 415] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-23 23:23:41 UTC · history