Properties

Label 2.173.abt_bgg
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:  $1 - 45 x + 838 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0154486843224$, $\pm0.247870790543$
Angle rank:  $2$ (numerical)
Number field:  4.0.1806444.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22938 885360924 26801759572056 802360164759947136 24013778529438943026018 718709000431308768206228736 21510248278619325568734388129362 643780248519041816573257694970637824 19267699135292190124750962834299702512344 576662967575038684592778661076500570190273724

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29581 5176368 895746145 154963702869 26808743828122 4637914106334393 802359175029023329 138808137837378759264 24013807852316095005061

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.1806444.1.
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_bgg$2$(not in LMFDB)