Properties

Label 1.512.bh
Base Field $\F_{2^{9}}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{9}}$
Dimension:  $1$
L-polynomial:  $1 + 33 x + 512 x^{2}$
Frobenius angles:  $\pm0.760109405386$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-959}) \)
Galois group:  $C_2$

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 a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 546 262080 134202978 68719996800 35184362479266 18014398560325440 9223372040097040098 4722366482736618643200 2417851639231988186922786 1237940039285358299865374400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 546 262080 134202978 68719996800 35184362479266 18014398560325440 9223372040097040098 4722366482736618643200 2417851639231988186922786 1237940039285358299865374400

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{9}}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-959}) \).
All geometric endomorphisms are defined over $\F_{2^{9}}$.

Base change

This is a primitive isogeny class.

Twists

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