Properties

Label 2.173.abw_bjk
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:  $1 - 48 x + 920 x^{2} - 8304 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0831146155212$, $\pm0.171345404759$
Angle rank:  $2$ (numerical)
Number field:  4.0.536832.2
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 22498 881966596 26793105621394 802361733942391056 24013885723989916596898 718709530613657606323002052 21510249971801609547107660490514 643780252564387255628699778557411328 19267699142570663362614951986149802622178 576662967583913805619633520289169884578176516

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 126 29466 5174694 895747894 154964394606 26808763604586 4637914471408470 802359180070836958 138808137889814252958 24013807852685679082746

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.536832.2.
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.bw_bjk$2$(not in LMFDB)