Properties

Label 2.173.abw_bjj
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:  $1 - 48 x + 919 x^{2} - 8304 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0666081623220$, $\pm0.178705272832$
Angle rank:  $2$ (numerical)
Number field:  4.0.843408.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22497 881904897 26792358779124 802356772797220329 24013861995771846125097 718709439640694857101034128 21510249678029729135864313918753 643780251748117612428677808774438537 19267699140617273278542122171735800944468 576662967579990368780175403687391452062930897

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 29464 5174550 895742356 154964241486 26808760211182 4637914408067094 802359179053500004 138808137875741662446 24013807852522296546184

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.843408.1.
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.bw_bjj$2$(not in LMFDB)