Properties

Label 2.173.abv_bin
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:  $1 - 47 x + 897 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.114645392612$, $\pm0.176096830998$
Angle rank:  $2$ (numerical)
Number field:  4.0.410525.1
Galois group:  $D_{4}$
Jacobians:  19

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 19 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22649 883424245 26799758770301 802384333405685525 24013949178262395007744 718709682968103252217775005 21510250283801390593361075618741 643780253080184692226376171793163525 19267699143096311217707555665128607330169 576662967583346956184144079983495140361728000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29515 5175979 895773123 154964804082 26808769287595 4637914538680039 802359180713688003 138808137893601119227 24013807852662073936950

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.410525.1.
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.bv_bin$2$(not in LMFDB)