# Properties

 Label 3.13.ap_ef_asv 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: $1 - 15 x + 109 x^{2} - 489 x^{3} + 1417 x^{4} - 2535 x^{5} + 2197 x^{6}$ Frobenius angles: $\pm0.0482491347716$, $\pm0.243527616942$, $\pm0.379270569548$ Angle rank: $3$ (numerical) Number field: 6.0.296888383.1 Galois group: $S_4\times C_2$

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 $A(\F_{q^r})$ 685 4632655 10907274865 23331278233575 51035015651132425 112338752869076393455 247025864572125233807680 542787728252166194461755975 1192515679248513143466178585885 2619980793491707865286568425897775

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 163 2261 28603 370199 4821799 62738696 815711123 10604342747 137857710463

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is 6.0.296888383.1.
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.p_ef_sv $2$ (not in LMFDB)