Properties

Label 1.193.ay
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:  $1 - 24 x + 193 x^{2}$
Frobenius angles:  $\pm0.168091317575$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-1}) \)
Galois group:  $C_2$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 170 37060 7189130 1387526400 267786091850 51682554922180 9974730495777770 1925122954219545600 371548729911809905130 71708904872990668015300

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 170 37060 7189130 1387526400 267786091850 51682554922180 9974730495777770 1925122954219545600 371548729911809905130 71708904872990668015300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{193}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1}) \).
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
1.193.y$2$(not in LMFDB)
1.193.ao$4$(not in LMFDB)
1.193.o$4$(not in LMFDB)