curve #6394

y² + xy = x³ − 16459890346736115847715250x + 25705583868845310042756279588957562500

a-invariants: [1, 0, 0, -16459890346736115847715250, 25705583868845310042756279588957562500]
c-invariants: [790074736643333560690332001, -22209624462683532989046390565200369498001]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/3ℤ
conductor (N): 12179989966747952083343629383030
discriminant (Δ): -51201457123182158038594651768591235679362288296412968225443938304000000000
Faltings height: 13.1758
naive height: 185.8027
primes of bad reduction: 2, 3, 5, 17, 19, 103, 181, 233, 337, 613, 661, 1567, 3307, 21523
regulator: 96791469475.26889431196396536293886668006564998787209539265
submitted by: Maksym Voznyy
submitted at: 2026-11-02 01:16:01 UTC
last updated: 2026-11-02 01:16:01 UTC

Witness: 10 independent points log in to add more points →

(60481077998682507300/24334489, 46341335566966125403027815750/120042034237)
(211900819777873393140/90801841, 46076382612194601397978119150/865250742889)
(1017552185497059300/466489, 135326783610311577508028250/318611987)
(129865786779500/49, -286561456731784780750/343)
(14730756837355140/6241, 33362588700859187152290/493039)
(5870940705540, 11464280888564842110)
(4704604551380924302500/1728979561, 74165987417148105549636624297750/71892699125941)
(61511842627544562660/37687321, -413121319562918949910350576390/231362463619)
(160759522821012750/2209, -64358171327837955851136000/103823)
(11271927448948514330177910/4829142495961, 559366579047409201522292497981588440/10612190338291672291)

Commentary

Voznyy (2026), T = -225/136 for the rank-5 fibration of X163 given by y^2 + (9T^2 - 6T + 244)xy + (13T - 90)(22T - 15)(5T + 6)(4T + 15)y = x^3 mentioned in the curve#4645

last edited by Maksym Voznyy at 2026-11-02 01:16:01 UTC · history