curve #1897

y² + xy + y = x³ + x² − 181610456457528727484901576033932410117420x + 28237703990352298099343957170848183918831345880437119331127757

a-invariants: [1, 1, 1, -181610456457528727484901576033932410117420, 28237703990352298099343957170848183918831345880437119331127757]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/8ℤ
conductor (N): 4738696264040550563800319661390
discriminant (Δ): 38893284316070022047117279980982379262598153745883666080388917582600495276490106959080126552814134734505028563430391483040000
Faltings height: 22.6599
naive height: 296.6217
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 29, 41, 71, 113, 193, 1889, 171679, 818231
regulator: 14689115.332253456265418855995967100974705623371279
submitted by: dujella
submitted at: 2026-09-25 17:48:14 UTC
last updated: 2026-09-25 17:48:14 UTC

(-262111421981438149703, -7604748244761082296499240767399)
(1603280928397240856483/4, 35632863910443103768825980795453/8)
(-457186661814710830273, -3963153939885314844704500853109)
(-224502275521833029363287/529, -65380881667793259648646887167612433/12167)
(353962605247773224817, 2881353967164064571433334624921)
(10252458713508502560373/9, 973361599099440081832010470975427/27)

found by Voznyy (2021)

last edited by dujella at 2026-09-25 17:48:15 UTC · history