Properties

Label 2.173.abt_bgu
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 173 x^{2} )( 1 - 22 x + 173 x^{2} )$
Frobenius angles:  $\pm0.161302001611$, $\pm0.184705758688$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

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
$A(\F_{q^r})$ 22952 886222624 26811559478144 802419360182962816 24014026503592729765832 718709793140405860274661376 21510250262498122733322611579528 643780252265210088651077555367074304 19267699139601012098947827640708302935936 576662967572931989059166738770216089270286624

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29609 5178258 895812225 154965303069 26808773397158 4637914534086753 802359179697965089 138808137868420325274 24013807852228366497089

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The isogeny class factors as 1.173.ax $\times$ 1.173.aw 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 $\F_{173}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.173.ab_age$2$(not in LMFDB)
2.173.b_age$2$(not in LMFDB)
2.173.bt_bgu$2$(not in LMFDB)