# Properties

 Label 3.11.ap_ea_aqq 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: $( 1 - 6 x + 11 x^{2} )( 1 - 9 x + 39 x^{2} - 99 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.100899808413$, $\pm0.140218899004$, $\pm0.366706655625$ Angle rank: $3$ (numerical)

This isogeny class is not 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 $A(\F_{q^r})$ 318 1539756 2374722558 3138798765024 4171825565612448 5563216585745102700 7406323568281759240038 9853404054619142247744384 13111195936794203960314102422 17449575838115732438710086890496

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 105 1341 14641 160842 1772613 19503159 214438769 2358163827 25937682600

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.aj_bn and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_ae_bk $2$ (not in LMFDB) 3.11.d_ae_abk $2$ (not in LMFDB) 3.11.p_ea_qq $2$ (not in LMFDB)