Properties

Label 2.19.al_cj
Base Field $\F_{19}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{19}$
Dimension:  $2$
Weil polynomial:  $1 - 11 x + 61 x^{2} - 209 x^{3} + 361 x^{4}$
Frobenius angles:  $\pm0.111054296713$, $\pm0.3956338348$
Angle rank:  $2$ (numerical)
Number field:  4.0.508805.3
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 203 130529 47425469 16943316845 6124641547248 2213387850962561 799087621661019593 288449415785418438005 104127647414623118474279 37589971930139626308751104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 363 6915 130011 2473504 47047431 893962281 16984034211 322688618535 6131066008678

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.