Properties

Label 2.173.abx_bkh
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:  $1 - 49 x + 943 x^{2} - 8477 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.00490035885878$, $\pm0.168696723871$
Angle rank:  $2$ (numerical)
Number field:  4.0.4901.1
Galois group:  $D_{4}$
Jacobians:  1

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 1 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22347 880449453 26785675847151 802333646980137909 24013793759339872015632 718709256201002043711102525 21510249203894161128150642364143 643780250512586676553517966276021349 19267699137276561216105319969067225091099 576662967570640207193574799312233312020713728

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 125 29415 5173259 895716539 154963801150 26808753368655 4637914305836755 802359177513627379 138808137851674542797 24013807852132930492950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.4901.1.
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_bkh$2$(not in LMFDB)