Properties

Label 2.173.abt_bgk
Base Field $\F_{173}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 45 x + 842 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0683613928513$, $\pm0.237830868262$
Angle rank:  $2$ (numerical)
Number field:  4.0.208444.1
Galois group:  $D_{4}$
Jacobians:  18

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

This isogeny class contains the Jacobians of 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22942 885607084 26804559443944 802377149287432896 24013850773800021375382 718709241032789744198738176 21510248944260013690520681894998 643780250125101329523931652675261184 19267699138904804177151254551529223616936 576662967583401714179572636406416912188109324

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29589 5176908 895765105 154964169069 26808752802858 4637914249855953 802359177030694849 138808137863404712124 24013807852664354208189

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.208444.1.
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.bt_bgk$2$(not in LMFDB)