Properties

Label 2.173.abt_bgn
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:  $1 - 45 x + 845 x^{2} - 7785 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0929373847626$, $\pm0.228622914131$
Angle rank:  $2$ (numerical)
Number field:  4.0.14449221.1
Galois group:  $D_{4}$
Jacobians:  40

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 40 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22945 885791725 26806659400885 802389850119073125 24013904224903563739600 718709414066605010637931525 21510249391396228958324472012565 643780251045365096868829651029673125 19267699140334661694896279357913658073305 576662967584748389869045820466864724887040000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 129 29595 5177313 895779283 154964513994 26808759257235 4637914346264853 802359178177642243 138808137873705675309 24013807852720433431350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.14449221.1.
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_bgn$2$(not in LMFDB)