# Properties

 Label 3.13.aq_eq_aux 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: $1 - 16 x + 120 x^{2} - 543 x^{3} + 1560 x^{4} - 2704 x^{5} + 2197 x^{6}$ Frobenius angles: $\pm0.0186782147920$, $\pm0.208870362755$, $\pm0.359149016839$ Angle rank: $3$ (numerical) Number field: 6.0.9709203.1 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 $A(\F_{q^r})$ 615 4391715 10769211495 23323805483475 51056734370604075 112340505835142908155 247017510590676700158255 542782457877041823738771075 1192509017310997013503638712320 2619966322644293656283832526776075

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 154 2233 28594 370358 4821877 62736574 815703202 10604283508 137856949034

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{13}$
 The endomorphism algebra of this simple isogeny class is 6.0.9709203.1.
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_eq_ux $2$ (not in LMFDB)