# Properties

 Label 3.11.ao_dr_apc 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: $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 36 x^{2} - 88 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.196063835166$, $\pm0.372536541753$ 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 $A(\F_{q^r})$ 372 1700784 2487136572 3191106184704 4191399146410932 5568186683287825200 7406020776080204590908 9852036735821877591146496 13110203349394585193168206452 17449111854549923398582228930224

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 116 1402 14884 161598 1774196 19502362 214409020 2357985310 25936992916

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.ai_bk 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.ac_ab_bo $2$ (not in LMFDB) 3.11.c_ab_abo $2$ (not in LMFDB) 3.11.o_dr_pc $2$ (not in LMFDB)