Properties

Label 3.23.ax_je_acdp
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:  $( 1 - 9 x + 23 x^{2} )( 1 - 14 x + 89 x^{2} - 322 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.0548738090170$, $\pm0.112386341891$, $\pm0.342656554695$
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
$A(\F_{q^r})$ 4245 133781175 1789206983280 21870536455411875 266408658624871575975 3243631005102834877766400 39471739028207398892139025785 480255730867373739945930612916875 5843227986782784329284038015386439120 71094377651935416144764571977462463729375

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 477 12088 279277 6430871 148012164 3404838809 78311795189 1801157883544 41426528030757

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.ao_dl 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_ao_gb$2$(not in LMFDB)
3.23.f_ao_agb$2$(not in LMFDB)
3.23.x_je_cdp$2$(not in LMFDB)