Properties

Label 2.5.ad_f
Base Field $\F_{5}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{5}$
Dimension:  $2$
Weil polynomial:  $1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.113143297209$, $\pm0.585923223955$
Angle rank:  $2$ (numerical)
Number field:  4.0.37845.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

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

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
$A(\F_{q^r})$ 13 637 12649 372645 10187008 246060997 6096639289 153327393765 3823723851493 95368161021952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 3 27 99 595 3258 15747 78039 392515 1957743 9765702

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.