# Properties

 Label 3.11.ao_dq_aox 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: $1 - 14 x + 94 x^{2} - 387 x^{3} + 1034 x^{4} - 1694 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0887296077117$, $\pm0.207434636458$, $\pm0.384783505598$ Angle rank: $3$ (numerical) Number field: 6.0.59264075.1 Galois group: $A_4\times C_2$

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 $A(\F_{q^r})$ 365 1662575 2435836625 3154139198075 4174009280277875 5562052815248264375 7403914687828017042685 9851215672838615019917075 13109998683927496431864536000 17449202308396969907023369109375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 114 1375 14714 160928 1772241 19496818 214391154 2357948500 25937127374

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.59264075.1.
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.o_dq_ox $2$ (not in LMFDB)