Properties

Label 3.23.ax_ji_acez
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 93 x^{2} - 322 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.159380640241$, $\pm0.302130010970$
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 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
$A(\F_{q^r})$ 4305 136240335 1814329989360 22002220775841075 266837831376550576275 3244513159378067756256000 39472643340755411955757410045 480255369579683167363482050829675 5843227061888887236240622663388489040 71094384856645752858025824689556577523175

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 485 12256 280957 6441231 148052420 3404916817 78311736277 1801157598448 41426532228925

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.ao_dp 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.23.af_ak_hl$2$(not in LMFDB)
3.23.f_ak_ahl$2$(not in LMFDB)
3.23.x_ji_cez$2$(not in LMFDB)