Properties

Label 2.193.abw_bku
Base Field $\F_{193}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 956 x^{2} - 9264 x^{3} + 37249 x^{4}$
Frobenius angles:  $\pm0.0990880211071$, $\pm0.217437428422$
Angle rank:  $2$ (numerical)
Number field:  4.0.12830976.1
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
$A(\F_{q^r})$ 28894 1372985092 51677370931054 1925184719481016464 71709167718882851495374 2671085643074096602959820996 99495246077097509472069346395262 3706098384453445341660191495197593600 138048458699543876894729900888626122466366 5142167038130571923099034900005008448210442052

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36858 7188338 1387532518 267786165746 51682553037978 9974730426315794 1925122953229588606 371548729911508455314 71708904873357089622618

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is 4.0.12830976.1.
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.193.bw_bku$2$(not in LMFDB)