# Properties

 Label 3.11.ap_ed_ari 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: $( 1 - 6 x + 11 x^{2} )( 1 - 5 x + 11 x^{2} )( 1 - 4 x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.228229222880$, $\pm0.293962833700$ 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 $A(\F_{q^r})$ 336 1645056 2523931200 3244050432000 4210466656559856 5564432369986560000 7399286919470169340176 9849227444670893948928000 13110067747977003449539588800 17449543701078556036959822260736

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -3 111 1422 15127 162327 1773000 19484637 214347887 2357960922 25937634831

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.af $\times$ 1.11.ae 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 are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.ah_t_abi $2$ (not in LMFDB) 3.11.af_h_k $2$ (not in LMFDB) 3.11.ad_ab_cc $2$ (not in LMFDB) 3.11.d_ab_acc $2$ (not in LMFDB) 3.11.f_h_ak $2$ (not in LMFDB) 3.11.h_t_bi $2$ (not in LMFDB) 3.11.p_ed_ri $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.ah_t_abi $2$ (not in LMFDB) 3.11.af_h_k $2$ (not in LMFDB) 3.11.ad_ab_cc $2$ (not in LMFDB) 3.11.d_ab_acc $2$ (not in LMFDB) 3.11.f_h_ak $2$ (not in LMFDB) 3.11.h_t_bi $2$ (not in LMFDB) 3.11.p_ed_ri $2$ (not in LMFDB)