Properties

Label 2.173.abt_bgj
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:  $1 - 45 x + 841 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0590786929552$, $\pm0.240534632429$
Angle rank:  $2$ (numerical)
Number field:  4.0.191725.1
Galois group:  $D_{4}$
Jacobians:  35

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 35 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22941 885545541 26803859468409 802372908521883861 24013832817305137718736 718709181942676607802142461 21510248785309415991362202400689 643780249764445143252691443564214725 19267699138186850674765669970737636831821 576662967582032624842161882281642449465552896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29587 5176773 895760371 154964053194 26808750598723 4637914215583953 802359176581200163 138808137858232439709 24013807852607341620022

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.191725.1.
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_bgj$2$(not in LMFDB)