Properties

Label 3.23.aw_ip_abzt
Base Field $\F_{23}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{23}$
Dimension:  $3$
L-polynomial:  $( 1 - 9 x + 23 x^{2} )( 1 - 13 x + 83 x^{2} - 299 x^{3} + 529 x^{4} )$
Frobenius angles:  $\pm0.112386341891$, $\pm0.130958063173$, $\pm0.355407705965$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4515 137820375 1806401347380 21928162286559375 266613459226638913200 3244357759024573999038000 39473899786985947310825588805 480260443804406065546525132959375 5843234186065367837900250045030505620 71094377937417127735866067458289490400000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 492 12203 280012 6435817 148045329 3405025192 78312563684 1801159794449 41426528197107

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The isogeny class factors as 1.23.aj $\times$ 2.23.an_df 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.ae_al_ft$2$(not in LMFDB)
3.23.e_al_aft$2$(not in LMFDB)
3.23.w_ip_bzt$2$(not in LMFDB)