Properties

Label 2.173.abs_bfh
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:  $1 - 44 x + 813 x^{2} - 7612 x^{3} + 29929 x^{4}$
Frobenius angles:  $\pm0.0375459716603$, $\pm0.262163108058$
Angle rank:  $2$ (numerical)
Number field:  4.0.1031441.3
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 23087 886517713 26805103355456 802364410055806169 24013774776519431260207 718708981183397160425574400 21510248322312823403258491712423 643780249070501381190263436874735529 19267699137711595346060554251211283392064 576662967582056227103242852026165030098661553

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 130 29620 5177014 895750884 154963678650 26808743110150 4637914115755330 802359175716320964 138808137854808610702 24013807852608324482100

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{173}$
The endomorphism algebra of this simple isogeny class is 4.0.1031441.3.
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.bs_bfh$2$(not in LMFDB)