curve #467

y² + xy = x³ − 1375414938269729933430x + 20780863582673042643051322404516

a-invariants: [1, 0, 0, -1375414938269729933430, 20780863582673042643051322404516]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 158140808443633262248097342764249526170467053622 ★ record for rank ≥ 17
discriminant (Δ): -20031065768099044318129751351987585821224786002547000120802541568
Faltings height: 11.0891
naive height: 157.7463
primes of bad reduction: 2, 3, 11, 19, 281, 1019, 295571, 3131017, 40764215801, 1061321324856931
regulator: 47341193300790.9314564139860297588904874677256530023040092847884030074541
submitted by: Rayan Hatout
submitted at: 2026-08-31 09:26:55 UTC
last updated: 2026-08-31 09:26:55 UTC

(-1070034385738848399228/854731683289, 3748379178032800358814734608279482/790213971639296413)
(2845905231300, 4800581405653755354)
(96790231284, 28185387341617050)
(93317365140, -26552835059912166)
(11517047786031/4, -39081933413961053667/8)
(114108374148, 36736951677214938)
(49788553848, -8701851926201862)
(50185952993364/25, -355467457002085630422/125)
(1148628456810/49, -408770576301028782/343)
(80374094646, -20723200900312674)
(6727113475980/169, 11852032382393095842/2197)
(5234522640696/289, -6611054491297921062/4913)
(11177636197164/289, -24780851513415213702/4913)
(32066156418, 3106146551017758)
(66780146916, -15058001222349222)
(47034389544, -7755030151177314)
(1387784521932/49, -731213426215148106/343)

Mestre ten-root construction roots 0,8,12,20,23,29,34,44,48,58

last edited by Rayan Hatout at 2026-08-31 09:26:55 UTC · history