Properties

Label 2.256.acd_bwq
Base Field $\F_{2^{8}}$
Dimension $2$
Ordinary No
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{8}}$
Dimension:  $2$
L-polynomial:  $1 - 55 x + 1264 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.125067363196$, $\pm0.207496263663$
Angle rank:  $2$ (numerical)
Number field:  4.0.63869.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple.

Newton polygon

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

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
$A(\F_{q^r})$ 52666 4262575376 281474077892554 18447229100083951904 1208928994155963380141626 79228175984148871052894286896 5192296900052207453694194099922346 340282367003070684188708837123845926464 22300745198536194826875455890760405481625114 1461501637330193672582505413593870250587671344976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65040 16777162 4295080224 1099514515002 281475024565296 72057594614097322 18446744078161948224 4722366482870825063962 1208925819614042500478800

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.63869.1.
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_bwq$2$(not in LMFDB)