# Properties

 Label 3.13.aq_es_avj Base Field $\F_{13}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{13}$ Dimension: $3$ L-polynomial: $1 - 16 x + 122 x^{2} - 555 x^{3} + 1586 x^{4} - 2704 x^{5} + 2197 x^{6}$ Frobenius angles: $\pm0.107742898637$, $\pm0.227592439174$, $\pm0.325764106975$ Angle rank: $3$ (numerical) Number field: 6.0.11666459.1 Galois group: $A_4\times C_2$

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 631 4531211 11072490799 23666737082339 51292846885738891 112441506056786691707 247051516374572851920007 542815558600951600440704579 1192556086446545013697266713152 2620009943543046531274372722139691

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 158 2293 29010 372068 4826213 62745212 815752946 10604702068 137859244278

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is 6.0.11666459.1.
All geometric endomorphisms are defined over $\F_{13}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.13.q_es_vj $2$ (not in LMFDB)