Properties

Label 2.256.ace_bxt
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:  $1 - 56 x + 1293 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.120560706820$, $\pm0.193487102895$
Angle rank:  $2$ (numerical)
Number field:  4.0.6733584.3
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
$A(\F_{q^r})$ 52438 4259119236 281451515095582 18447139553571928896 1208928845236721888497798 79228176874401087016470741924 5192296909746238942811217225085582 340282367054656146887422965541710169344 22300745198710282447222324142473883759404342 1461501637330422794513980164159027838086136004676

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64987 16775817 4295059375 1099514379561 281475027728107 72057594748629033 18446744080958401759 4722366482907689551497 1208925819614232025698427

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.6733584.3.
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.ce_bxt$2$(not in LMFDB)