Properties

Label 1.193.c
Base Field $\F_{193}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{193}$
Dimension:  $1$
L-polynomial:  $1 + 2 x + 193 x^{2}$
Frobenius angles:  $\pm0.522932279470$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$
Jacobians:  16

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

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
$A(\F_{q^r})$ 196 37632 7187908 1387416576 267785548996 51682553604864 9974730229487044 1925122950592278528 371548729936643739844 71708904873681426930432

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 196 37632 7187908 1387416576 267785548996 51682553604864 9974730229487044 1925122950592278528 371548729936643739844 71708904873681426930432

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).
All geometric endomorphisms are defined over $\F_{193}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
1.193.ac$2$(not in LMFDB)
1.193.az$3$(not in LMFDB)
1.193.x$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.193.ac$2$(not in LMFDB)
1.193.az$3$(not in LMFDB)
1.193.x$3$(not in LMFDB)
1.193.ax$6$(not in LMFDB)
1.193.z$6$(not in LMFDB)