# Properties

 Label 3.13.ap_ed_ash 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: $1 - 15 x + 107 x^{2} - 475 x^{3} + 1391 x^{4} - 2535 x^{5} + 2197 x^{6}$ Frobenius angles: $\pm0.0356147865305$, $\pm0.203805463241$, $\pm0.408190245538$ Angle rank: $3$ (numerical) Number field: 6.0.279340175.1 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 $A(\F_{q^r})$ 671 4509791 10676155523 23168460479879 51044453464796891 112437272100305768759 247090793820651893465408 542787389009674883450894375 1192488803215307020031633525831 2619961820501932501511744178896831

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 159 2213 28403 370269 4826031 62755188 815710611 10604103749 137856712139

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is 6.0.279340175.1.
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_ed_sh $2$ (not in LMFDB)