Properties

Label 1.347.av
Base Field $\F_{347}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{347}$
Dimension:  $1$
L-polynomial:  $1 - 21 x + 347 x^{2}$
Frobenius angles:  $\pm0.309389154117$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-947}) \)
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
$A(\F_{q^r})$ 327 120663 41794524 14498504091 5030918907297 1745729014381776 605767992733168347 210201493944724085043 72939918400026151288068 25310151684672608076171543

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 327 120663 41794524 14498504091 5030918907297 1745729014381776 605767992733168347 210201493944724085043 72939918400026151288068 25310151684672608076171543

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{347}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-947}) \).
All geometric endomorphisms are defined over $\F_{347}$.

Base change

This is a primitive isogeny class.

Twists

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