# Properties

 Label 3.11.an_cy_alf 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: $1 - 13 x + 76 x^{2} - 291 x^{3} + 836 x^{4} - 1573 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0354721676546$, $\pm0.103262097857$, $\pm0.494210615205$ Angle rank: $3$ (numerical) Number field: 6.0.2343728.1 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 $A(\F_{q^r})$ 367 1512407 2178396028 3027725383475 4158835374916837 5564732250376667888 7400452781633010860183 9848705743351045280314475 13110142522400296216941219508 17449735445916943529157064457567

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 105 1226 14117 160339 1773096 19487705 214336533 2357974370 25937919845

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.2343728.1.
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_cy_lf $2$ (not in LMFDB)