# Properties

 Label 3.11.an_de_ams Base Field $\F_{11}$ Dimension $3$ Ordinary No $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $1 - 13 x + 82 x^{2} - 330 x^{3} + 902 x^{4} - 1573 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0593713135806$, $\pm0.214892189705$, $\pm0.437033929118$ Angle rank: $3$ (numerical) Number field: 6.0.5910179.1 Galois group: $S_4\times C_2$

This isogeny class is simple and geometrically simple.

## Newton polygon

 $p$-rank: $2$ Slopes: $[0, 0, 1/2, 1/2, 1, 1]$

## 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 $A(\F_{q^r})$ 400 1692800 2378443600 3110750220800 4167688334560000 5564540830268700800 7402622215673449240400 9848788048888092229683200 13108995802629252949856539600 17449185894269004447078379520000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 117 1343 14513 160684 1773033 19493417 214338321 2357768117 25937102972

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.5910179.1.
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_ms $2$ (not in LMFDB)