curve #2840

y² + xy + y = x³ − x² − 81998483989093847324602383387x + 9039662557314583503984236650851472967245899

a-invariants: [1, -1, 1, -81998483989093847324602383387, 9039662557314583503984236650851472967245899]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/7ℤ
conductor (N): 3370525273093188329210
discriminant (Δ): -15500778873511975969237368396719961290510947157765742994373613651486760999485440000000
Faltings height: 15.3328
naive height: 211.3435
primes of bad reduction: 2, 5, 7, 13, 17, 53, 71, 139, 223, 617, 3027389
regulator: 92395.8646525381893448549006239639721791967997984
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:24:49 UTC
last updated: 2026-09-26 20:24:49 UTC

(120758100624827, 947965475556972223546)
(-117778126528243, -4130799992267648976004)
(166003611484257, 47038619859647754246)
(292645587321907, 3178955262932679668346)
(-95474599855473557/289, -1331648350736416603324902/4913)

Eroshkin (2009). Source: https://dujella.github.io/tors/z7old5.html (curve entry 11). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:24:49 UTC · history