Properties

Label 1.353.abk
Base Field $\F_{353}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{353}$
Dimension:  $1$
L-polynomial:  $1 - 36 x + 353 x^{2}$
Frobenius angles:  $\pm0.0925328421223$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-29}) \)
Galois group:  $C_2$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 318 124020 43978446 15527304000 5481172669038 1934854160777460 683003514136150686 241100240250164256000 85108384801301949875358 30043259834692054754618100

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 318 124020 43978446 15527304000 5481172669038 1934854160777460 683003514136150686 241100240250164256000 85108384801301949875358 30043259834692054754618100

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{353}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-29}) \).
All geometric endomorphisms are defined over $\F_{353}$.

Base change

This is a primitive isogeny class.

Twists

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