curve #5605

y² = x³ − 51293867316482611612089675

a-invariants: [0, 0, 0, 0, -51293867316482611612089675]
c-invariants: [0, 44317901361440976432845479200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 205175469265930446448358700
discriminant (Δ): -1136618276089358768766167613249467306612619944373630000
Faltings height: 9.0512
naive height: 131.9224
primes of bad reduction: 2, 3, 5, 13, 37, 41, 59, 151, 523
regulator: 1158059818309.23550726682250967224717559717256202631791
submitted by: Maksym Voznyy
submitted at: 2026-10-23 22:25:47 UTC
last updated: 2026-10-23 22:25:47 UTC

(12005728687996697586019/24158630710449, -1003611505720359287221691874502472/118743124626048429207)
(3620944191546079454142323363608314196935169/1135911017893410258896964605345476, -6884756898819341955414168384898541988106086248241593292478222753/38283925998065207204152988271152677835735968145224)
(92052694999274757069324502474831/239490168957817370250849, -274681109279542773067064063935780287568427518546/117201058917270744391078977709546257)
(264045758073117279098421291506424869022303294049/145338636590890503297517836818013360400, 135099367814616999833057542516439571675523331775986355756433705615087343/1752151370548698303531342664859754751432661930946169192000)
(19460159489430243529700551/36084693322881225, 70423169851515463117114209476548015826/6854638059476920479850875)
(236082445383800088001980474012026423671/162818872493600458322032305625, 3596753452621840962035819441965173032587465480930800229906/65698751180011086480402350563165484931828125)
(42487224044184506860321/50720491036224, 8366809048790888660654011865184719/361222816117493242368)
(254827478285939307403073797999/55950672501713025, 128638031276711587277334861851504256727363682/13234513045595709626258625)

Voznyy (2023), A = 2756644963410, [r, s, t] = [-54, 39, 59] or [72, 185, 486] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 14:30:51 UTC · history