Properties

Label 2.256.ace_bxp
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:  $1 - 56 x + 1289 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0929357896899$, $\pm0.208872909793$
Angle rank:  $2$ (numerical)
Number field:  4.0.2816912.1
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
$A(\F_{q^r})$ 52434 4258584612 281440231225794 18447012761006965248 1208927847757902306575634 79228170824627393341910805348 5192296880751353668997287159117506 340282366949586117673888202626290321408 22300745198492476840117702716884850990343506 1461501637330940335408404756646101185454445716132

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64979 16775145 4295029855 1099513472361 281475006234995 72057594346244169 18446744075262544063 4722366482861567420169 1208925819614660125492499

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.2816912.1.
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.ce_bxp$2$(not in LMFDB)