curve #420

y² + xy = x³ − 181942231909583197148101236805013x + 997946339099553525501068395789161466011460824417

a-invariants: [1, 0, 0, -181942231909583197148101236805013, 997946339099553525501068395789161466011460824417]
rank (lower bound): ≥ 20
torsion subgroup: trivial
conductor (N): 4031074155710004840668767452186274375079456415080292049848958219089150
discriminant (Δ): -44766384314457424499180866941654319384332654293920066677529438416008346423517033096632312299520000
Faltings height: 17.4893
naive height: 234.5672
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 101, 16693029048719385849269, 1770656567753750040161244684435749933
regulator: 6518997735784251183.65803588738559505608079900814246676073094905879397375378305
submitted by: Bhavik Mehta
submitted at: 2026-08-29 17:01:50 UTC
last updated: 2026-08-29 17:01:50 UTC

Witness: 20 independent points log in to add more points →

(-11039195019921038, 1288861352146190567758999)
(6126955138525342, -336448757689971274428641)
(15519331660369042, -1382805192216695956025801)
(11582401349713042, -666649040933794806295241)
(10473944811831622, -491245418911664028292241)
(9996178041923922, -421987263488913592918281)
(16438927131986392, -1565068499875404068819351)
(7458269209482082, -236313846311926824529961)
(171567779534592562, -70851721352198794797029801)
(800730273901042, -923457140344946134699241)
(-14656556185209818, -718435831529155013134421)
(1945647571349746, 807041641612432025816599)
(6262918646105242, -322667947882037765287841)
(7512702697401022, 234713982755115157773919)
(46454143247092702, 9632934773259117530790019)
(2685446060955922, -727129086915301730094281)
(10777835440373122, 537563932579473796676119)
(7904250932251158, 231656235557297690475867)
(15470203064541346, -1373209089820761475723001)
(4667402230239142, -500426274760445806950101)

Commentary

From Elkies's rank-17 K3 fibration (arXiv:2608.25406), specialized at t = -22. The 3 points beyond the seventeen generic sections came from searching the 1311 norm-4 quartic covers.

last edited by Bhavik Mehta at 2026-08-29 17:01:50 UTC · history