# Properties

 Label 3.11.an_de_amr Base Field $\F_{11}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $1 - 13 x + 82 x^{2} - 329 x^{3} + 902 x^{4} - 1573 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0935398046292$, $\pm0.197577243604$, $\pm0.439402580349$ Angle rank: $3$ (numerical) Number field: 6.0.380456496.1 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 $A(\F_{q^r})$ 401 1696631 2385435116 3122053838019 4178977468600411 5571979389613552496 7406281847411912937481 9850277695137678031977099 13109520296723840105533567364 17449327630043840574870306343391

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 117 1346 14565 161119 1775400 19503049 214370741 2357862458 25937313657

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.380456496.1.
All geometric endomorphisms are defined over $\F_{11}$.

## 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 3.11.n_de_mr $2$ (not in LMFDB)