# Properties

 Label 3.11.ap_ee_arn 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: $( 1 - 5 x + 11 x^{2} )^{3}$ Frobenius angles: $\pm0.228229222880$, $\pm0.228229222880$, $\pm0.228229222880$ Angle rank: $1$ (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 $A(\F_{q^r})$ 343 1685159 2582630848 3291326171875 4233994921204433 5569931768213786624 7397215398464534471843 9846286021072917404296875 13108397687134511225731882048 17448991513836070999556906276039

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 113 1452 15341 163227 1774748 19479177 214283861 2357660532 25936814033

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af 3 and its endomorphism algebra is $\mathrm{M}_{3}($$$\Q(\sqrt{-19})$$$)$
All geometric endomorphisms are defined over $\F_{11}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.af_i_p $2$ (not in LMFDB) 3.11.f_i_ap $2$ (not in LMFDB) 3.11.p_ee_rn $2$ (not in LMFDB) 3.11.a_a_bo $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.af_i_p $2$ (not in LMFDB) 3.11.f_i_ap $2$ (not in LMFDB) 3.11.p_ee_rn $2$ (not in LMFDB) 3.11.a_a_bo $3$ (not in LMFDB) 3.11.af_o_ap $4$ (not in LMFDB) 3.11.f_o_p $4$ (not in LMFDB) 3.11.ak_by_agy $6$ (not in LMFDB) 3.11.a_a_abo $6$ (not in LMFDB) 3.11.k_by_gy $6$ (not in LMFDB)