Properties

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

Learn more about

Invariants

Base field:  $\F_{173}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 945 x^{2} - 8477 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0729523342082$, $\pm0.151505752657$
Angle rank:  $2$ (numerical)
Number field:  4.0.129725.1
Galois group:  $D_{4}$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22349 880572949 26787200771249 802344088938125141 24013845849262471846864 718709467600655259307104061 21510249940980768731405925454169 643780252788201642395077903559535749 19267699143607911499845008629114312169501 576662967586680769039266823753662786379853824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 125 29419 5173553 895728195 154964137290 26808761254123 4637914464763061 802359180349782339 138808137897286784129 24013807852800902933814

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.129725.1.
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.bx_bkj$2$(not in LMFDB)