Properties

Label 2.5.ad_f
Base Field $\F_{5}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5}$
Dimension:  $2$
L-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:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

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

Point counts

This isogeny class contains the Jacobians of 2 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The endomorphism algebra of this simple isogeny class is 4.0.37845.1.
All geometric endomorphisms are defined over $\F_{5}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.5.d_f$2$2.25.b_ap