# Properties

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

## Invariants

 Base field: $\F_{5}$ Dimension: $2$ L-polynomial: $( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$ Frobenius angles: $\pm0.265942140215$, $\pm0.352416382350$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

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

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 12 864 21312 432000 9689052 239376384 6059560092 152549568000 3817589596992 95392127486304

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 1 33 166 689 3101 15318 77561 390529 1954606 9768153

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ad $\times$ 1.5.ac and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.5.ab_e $2$ 2.25.h_ce 2.5.b_e $2$ 2.25.h_ce 2.5.f_q $2$ 2.25.h_ce
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.5.ab_e $2$ 2.25.h_ce 2.5.b_e $2$ 2.25.h_ce 2.5.f_q $2$ 2.25.h_ce 2.5.ah_w $4$ 2.625.cl_cwm 2.5.ab_ac $4$ 2.625.cl_cwm 2.5.b_ac $4$ 2.625.cl_cwm 2.5.h_w $4$ 2.625.cl_cwm