Properties

Label 1.32.aj
Base Field $\F_{2^{5}}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{5}}$
Dimension:  $1$
L-polynomial:  $1 - 9 x + 32 x^{2}$
Frobenius angles:  $\pm0.207210850837$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-47}) \)
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
$A(\F_{q^r})$ 24 1008 32904 1050336 33565944 1073789136 34359795816 1099510630848 35184361278168 1125899841448368

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1008 32904 1050336 33565944 1073789136 34359795816 1099510630848 35184361278168 1125899841448368

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{5}}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-47}) \).
All geometric endomorphisms are defined over $\F_{2^{5}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.32.j$2$1.1024.ar