# Properties

 Label 3.13.ap_ee_aso 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: $1 - 15 x + 108 x^{2} - 482 x^{3} + 1404 x^{4} - 2535 x^{5} + 2197 x^{6}$ Frobenius angles: $\pm0.0430990397297$, $\pm0.222225562473$, $\pm0.395227696733$ Angle rank: $3$ (numerical) Number field: 6.0.365587668.1 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 $A(\F_{q^r})$ 678 4571076 10791466326 23251344887424 51045199500731808 112395971660466168036 247063647712058721521382 542787046237881197925468672 1192498013715060193302368871702 2619967843446249868930769792664576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 161 2237 28505 370274 4824257 62748293 815710097 10604185655 137857029056

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is 6.0.365587668.1.
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_ee_so $2$ (not in LMFDB)