Properties

Label 2.256.acd_bwr
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:  $1 - 55 x + 1265 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.131627742141$, $\pm0.203215431612$
Angle rank:  $2$ (numerical)
Number field:  4.0.1129089.1
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
$A(\F_{q^r})$ 52667 4262708979 281476848410432 18447259346420378211 1208929221535385860330427 79228177263472738782126322944 5192296905372046711023176967686987 340282367016230370684695732622738151875 22300745198515935937780748853975126138043712 1461501637329708638620745693580325482239868011379

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65042 16777327 4295087266 1099514721802 281475029110367 72057594687924922 18446744078875336258 4722366482866535077327 1208925819613641289789202

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1129089.1.
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_bwr$2$(not in LMFDB)