Properties

Label 2.173.abt_bgm
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:  $1 - 45 x + 844 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0850578884700$, $\pm0.231907856828$
Angle rank:  $2$ (numerical)
Number field:  4.0.1007325.1
Galois group:  $D_{4}$
Jacobians:  80

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 80 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22944 885730176 26805959410176 802385620086007296 24013886477599203154464 718709357094432210483388416 21510249247294654495373909580576 643780250765437794358882532428339200 19267699139977511921507096561075469832704 576662967584750627470942998564295472114791296

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29593 5177178 895774561 154964399469 26808757132102 4637914315194513 802359177828761953 138808137871132700994 24013807852720526611153

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.1007325.1.
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.bt_bgm$2$(not in LMFDB)