Properties

Label 2.193.abw_bkw
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:  $( 1 - 26 x + 193 x^{2} )( 1 - 22 x + 193 x^{2} )$
Frobenius angles:  $\pm0.114714697559$, $\pm0.209145594264$
Angle rank:  $2$ (numerical)
Jacobians:  132

This isogeny class is not 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 132 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28896 1373137920 51679443983328 1925199672057446400 71709242656146423177696 2671085929339392785707576320 99495246924144591791008182420192 3706098386255186702829381999938764800 138048458701126347188380603836554426449632 5142167038122510997300036384834768080428313600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 36862 7188626 1387543294 267786445586 51682558576894 9974730511235090 1925122954165498366 371548729915767574418 71708904873244677840382

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The isogeny class factors as 1.193.aba $\times$ 1.193.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ae_ahe$2$(not in LMFDB)
2.193.e_ahe$2$(not in LMFDB)
2.193.bw_bkw$2$(not in LMFDB)