Properties

Label 2.173.abu_bhk
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:  $1 - 46 x + 868 x^{2} - 7958 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0714610774504$, $\pm0.218377440981$
Angle rank:  $2$ (numerical)
Number field:  4.0.7466816.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22794 884452788 26801372680650 802375204879051344 24013871929302929582154 718709349463788606310530900 21510249243189466990979511275466 643780250598982334844643192786351104 19267699138874008421826284855087239870650 576662967580529295698774574975578609780713428

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 128 29550 5176292 895762934 154964305588 26808756847470 4637914314309376 802359177621304414 138808137863182853696 24013807852544738922750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.7466816.1.
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.bu_bhk$2$(not in LMFDB)