curve #3563

y² + xy + y = x³ − 124516003883001484890743x + 16924795101824243077258212820413422

a-invariants: [1, 0, 1, -124516003883001484890743, 16924795101824243077258212820413422]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 11071590412635459962473009119576352361061912474190369886489478
discriminant (Δ): -192207304629059114945276202357548024987093391688409342519631252808068 ★ record for rank ≥ 20
Faltings height: 12.0269 ★ record for rank ≥ 20
naive height: 171.1513 ★ record for rank ≥ 20
primes of bad reduction: 2, 3, 7, 37658470791277074702289146665225688302931675082280169681937
regulator: 130275363866602537954.715001109493735466591015340025186227526577429044789596742
submitted by: Matej Jurasić
submitted at: 2026-09-28 15:23:26 UTC
last updated: 2026-09-28 15:23:26 UTC

(205430303544, 3863069705320498)
(258619589421, 44944878438138988)
(282800461668, -65794442351879114)
(1248623325933, -1344667926294510740)
(24136473498, -118040170674420224)
(799640407815/4, -37528520320317187/8)
(421218699351/4, 564575692469463809/8)
(76409637441, 88637904657622090)
(213030537378, -8175547133496584)
(-336557589112, -143907381443902635)
(-406883645094, -15065762405160347)
(254989624236, -41879204496811835)
(130813346256, 53618356448445178)
(-48641761857, 151216377537800170)
(298588083189, 79789411305081388)
(207913497999, 4891376232529858)
(213571925151, 8562699991043290)
(34631268504270/169, 8225096049760644172/2197)
(183954223026690/841, -302779977641444124856/24389)
(-4635999190191150/14161, 253343203819675542984419/1685159)

Specialization at T = -1/5 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751).

last edited by Matej Jurasić at 2026-09-28 15:23:26 UTC · history