Properties

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

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Invariants

Base field:  $\F_{5}$
Dimension:  $2$
Weil polynomial:  $1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4}$
Frobenius angles:  $\pm0.0878807261908$, $\pm0.450170915301$
Angle rank:  $2$ (numerical)
Number field:  4.0.4901.1
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
$A(\F_{q^r})$ 9 621 15093 353349 9460944 246815829 6158067813 152726271525 3813630612129 95424443559936

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 27 121 563 3026 15795 78821 390979 1952581 9771462

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.