curve #2018

y² = x³ + x² − 54128710278998744127227570207003233x + 4847185413158287793220272768281439445476477910377663

a-invariants: [0, 1, 0, -54128710278998744127227570207003233, 4847185413158287793220272768281439445476477910377663]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 207871256848409744593342350561253204800
discriminant (Δ): 795583344544664764303972590235535004991119606275080777471224142334339890146425507328000000
Faltings height: 18.1448
naive height: 251.5436
primes of bad reduction: 2, 3, 5, 13, 17, 23, 37, 41, 101, 359, 389, 541, 12479, 23209, 49411, 51431
regulator: 713821792862775.422994149722046305923863662939091079029923555
submitted by: Steps Unbounded
submitted at: 2026-09-26 05:01:12 UTC
last updated: 2026-09-26 05:01:12 UTC

Witness: 11 independent points log in to add more points →

(4868973444785824535153717/35844169, -206550525072816456214673002499522100/214599039803)
(134323878404684018, -2041280717927396475)
(2149339585262040113/16, 400140940747689199318575/64)
(5498468389022631735772397/40934404, 2508012418119231452873031984675/261898316792)
(1293667419253484178003818/9628609, -621190094584126008982740106550481/29877573727)
(1114266841967821912133/8281, -111570338305073504312487947700/753571)
(3612730934593397954085422018/26895672001, -4562246263252210283236297549974525/4410863312491999)
(36042324028604108502421/268324, 1498825690960309066269433233/138991832)
(36461009678795314490057/271441, -888615224740377916660936008/141420761)
(26999258958885200497137748757/436057924, 4436338794849194339629120917630358665849825/9105761568968)
(35826975529390057093111605925319522/6291023572936729, -6775763086934290915979407848527009446471276346756625/498978655853413128072317)

Commentary

Obtained by quotienting the rank-11 Z/2Z x Z/2Z curve of Dujella–Peral by the rational 2-torsion point with x-coordinate -67161937901586997. The 11 displayed points are the exact images of their independent rank-11 generators under the rational 2-isogeny.

last edited by Steps Unbounded at 2026-09-26 10:01:59 UTC · history