Properties

Label 2.256.ach_cbb
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:  $1 - 59 x + 1379 x^{2} - 15104 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0665684010103$, $\pm0.166976530011$
Angle rank:  $2$ (numerical)
Number field:  4.0.1915953.1
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
$A(\F_{q^r})$ 51753 4247834487 281364146256492 18446650244354507643 1208926666119019976288823 79228169023620522107959715088 5192296887778098980712502770093333 340282367015269500477963383627393542323 22300745198723784584629898212496897677051668 1461501637330873455821670349694447059136022536007

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 198 64814 16770609 4294945450 1099512397668 281474999836535 72057594443759850 18446744078823247378 4722366482910548740305 1208925819614604803994974

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1915953.1.
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.ch_cbb$2$(not in LMFDB)