Properties

Label 2.256.acd_bwn
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:  $1 - 55 x + 1261 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.107494201101$, $\pm0.217633038452$
Angle rank:  $2$ (numerical)
Number field:  4.0.38626289.1
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
$A(\F_{q^r})$ 52663 4262174579 281465766384400 18447138258070053779 1208928308389382311645603 79228172079822409671199640000 5192296883255098001680799278187023 340282366955447766321994130486099740739 22300745198532688336517670037429743810907600 1461501637331227152816181264556851190537451670059

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65034 16776667 4295059074 1099513891302 281475010694343 72057594380990602 18446744075580304674 4722366482870082535747 1208925819614897375291554

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.38626289.1.
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.cd_bwn$2$(not in LMFDB)