# Properties

 Label 3.11.aq_en_atd 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: $( 1 - 5 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.0215640055172$, $\pm0.228229222880$, $\pm0.270299311731$ 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 $A(\F_{q^r})$ 287 1488095 2408204372 3188429549375 4185769049802032 5552464513772202320 7393096432039702835437 9846257309200912727019375 13108906041999147831913733012 17449225520380929509044580000000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -4 100 1361 14876 161381 1769185 19468326 214283236 2357751971 25937161875

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af $\times$ 2.11.al_bz 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.ag_h_n $2$ (not in LMFDB) 3.11.g_h_an $2$ (not in LMFDB) 3.11.q_en_td $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.11.ag_h_n $2$ (not in LMFDB) 3.11.g_h_an $2$ (not in LMFDB) 3.11.q_en_td $2$ (not in LMFDB) 3.11.ag_h_x $5$ (not in LMFDB) 3.11.ag_bl_aex $5$ (not in LMFDB) 3.11.ab_ad_cg $5$ (not in LMFDB) 3.11.e_h_ah $5$ (not in LMFDB) 3.11.ao_dt_apn $10$ (not in LMFDB) 3.11.aj_bl_aeo $10$ (not in LMFDB) 3.11.ae_ad_cp $10$ (not in LMFDB) 3.11.ae_h_h $10$ (not in LMFDB) 3.11.ae_bb_adf $10$ (not in LMFDB) 3.11.b_ad_acg $10$ (not in LMFDB) 3.11.e_ad_acp $10$ (not in LMFDB) 3.11.e_bb_df $10$ (not in LMFDB) 3.11.g_h_ax $10$ (not in LMFDB) 3.11.g_bl_ex $10$ (not in LMFDB) 3.11.j_bl_eo $10$ (not in LMFDB) 3.11.o_dt_pn $10$ (not in LMFDB)