# Properties

 Label 3.23.aw_io_abzk Base Field $\F_{23}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes

## Invariants

 Base field: $\F_{23}$ Dimension: $3$ L-polynomial: $( 1 - 4 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ Frobenius angles: $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.363071407864$ 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 it is unknown whether it contains a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 4500 137214000 1800591768000 21901069575000000 266540777012295562500 3244254578261976964608000 39473880803843878445301679500 480260565857341590256158300000000 5843234256537895635557271282005448000 71094380852037326861596837323207336750000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 2 490 12164 279666 6434062 148040620 3405023554 78312583586 1801159816172 41426529895450

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The isogeny class factors as 1.23.aj 2 $\times$ 1.23.ae and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.23.aj 2 : $\mathrm{M}_{2}($$$\Q(\sqrt{-11})$$$)$ 1.23.ae : $$\Q(\sqrt{-19})$$.
All geometric endomorphisms are defined over $\F_{23}$.

## 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 3.23.ao_da_ami $2$ (not in LMFDB) 3.23.ae_am_fk $2$ (not in LMFDB) 3.23.e_am_afk $2$ (not in LMFDB) 3.23.o_da_mi $2$ (not in LMFDB) 3.23.w_io_bzk $2$ (not in LMFDB) 3.23.f_bt_ha $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 3.23.ao_da_ami $2$ (not in LMFDB) 3.23.ae_am_fk $2$ (not in LMFDB) 3.23.e_am_afk $2$ (not in LMFDB) 3.23.o_da_mi $2$ (not in LMFDB) 3.23.w_io_bzk $2$ (not in LMFDB) 3.23.f_bt_ha $3$ (not in LMFDB) 3.23.ae_cg_afk $4$ (not in LMFDB) 3.23.e_cg_fk $4$ (not in LMFDB) 3.23.an_en_ayw $6$ (not in LMFDB) 3.23.af_bt_aha $6$ (not in LMFDB) 3.23.n_en_yw $6$ (not in LMFDB)