Properties

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

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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.

Point counts of the abelian variety

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

Point counts of the (virtual) curve

$r$ 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:
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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)