Properties

Label 2.256.acd_bwf
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:  $1 - 55 x + 1253 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0614721139001$, $\pm0.236081656579$
Angle rank:  $2$ (numerical)
Number field:  4.0.2623305.2
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
$A(\F_{q^r})$ 52655 4261105875 281443602695120 18446895257327125875 1208926453070853840633875 79228161181088392748594904000 5192296832291171388575870090139095 340282366767985342960126555983144295875 22300745198038854004261055546816108377636880 1461501637330714695455091802409807703185463046875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65018 16775347 4295002498 1099512203902 281474971974263 72057593673724042 18446744065417946338 4722366482765509048267 1208925819614473480497698

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.2623305.2.
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_bwf$2$(not in LMFDB)