Properties

Label 2.256.acc_bvf
Base Field $\F_{2^{8}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $1 - 54 x + 1227 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0895618621667$, $\pm0.240995948916$
Angle rank:  $2$ (numerical)
Number field:  4.0.119597632.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

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
$A(\F_{q^r})$ 52886 4264832812 281472263613650 18447060931863868000 1208927287272962147705606 79228165215875823037375026700 5192296852116787945679581479679586 340282366866175465531987285849623792000 22300745198503142392024416198685011921927350 1461501637332677702818677039557370214227532103212

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65075 16777055 4295041071 1099512962603 281474986308707 72057593948859743 18446744070740843551 4722366482863825938635 1208925819616097242131155

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.119597632.1.
All geometric endomorphisms are defined over $\F_{2^{8}}$.

Base change

This is a primitive isogeny class.

Twists

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