Properties

Label 2.173.abv_bij
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:  $1 - 47 x + 893 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0630646735849$, $\pm0.201502091012$
Angle rank:  $2$ (numerical)
Number field:  4.0.2863413.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22645 883177645 26796833870065 802365499477709125 24013862943484532473600 718709371604288605548056245 21510249359225606911303901531905 643780250809760580674312082385225125 19267699138667509260125728103605546876045 576662967577654628172930391898626162055065600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 127 29507 5175415 895752099 154964247602 26808757673339 4637914339328411 802359177884002531 138808137861695194795 24013807852425029980982

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.2863413.1.
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_bij$2$(not in LMFDB)