# Properties

 Label 3.11.an_dd_amk 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: $( 1 - x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$ Frobenius angles: $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.451829325548$ Angle rank: $2$ (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 $A(\F_{q^r})$ 396 1667952 2355076944 3115894459392 4187575203146676 5579766049572000000 7409873167779616546716 9851755237142869229617152 13110200328368082527594077104 17449545804474034197334210288752

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 115 1328 14535 161449 1777876 19512499 214402895 2357984768 25937637955

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag 2 $\times$ 1.11.ab and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.11.ag 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-2})$$$)$ 1.11.ab : $$\Q(\sqrt{-43})$$.
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.al_cf_ahy $2$ (not in LMFDB) 3.11.ab_ad_o $2$ (not in LMFDB) 3.11.b_ad_ao $2$ (not in LMFDB) 3.11.l_cf_hy $2$ (not in LMFDB) 3.11.n_dd_mk $2$ (not in LMFDB) 3.11.f_be_ed $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.al_cf_ahy $2$ (not in LMFDB) 3.11.ab_ad_o $2$ (not in LMFDB) 3.11.b_ad_ao $2$ (not in LMFDB) 3.11.l_cf_hy $2$ (not in LMFDB) 3.11.n_dd_mk $2$ (not in LMFDB) 3.11.f_be_ed $3$ (not in LMFDB) 3.11.ab_z_ao $4$ (not in LMFDB) 3.11.b_z_o $4$ (not in LMFDB) 3.11.ah_bq_agb $6$ (not in LMFDB) 3.11.af_be_aed $6$ (not in LMFDB) 3.11.h_bq_gb $6$ (not in LMFDB) 3.11.af_x_ads $8$ (not in LMFDB) 3.11.ad_p_adc $8$ (not in LMFDB) 3.11.d_p_dc $8$ (not in LMFDB) 3.11.f_x_ds $8$ (not in LMFDB)