Properties

Label 2.256.ace_bxl
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:  $1 - 56 x + 1285 x^{2} - 14336 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0659015562322$, $\pm0.219579078510$
Angle rank:  $2$ (numerical)
Number field:  4.0.34741520.2
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
$A(\F_{q^r})$ 52430 4258050020 281428947479750 18446885693771958080 1208926840427672387190750 79228164590296342012940418500 5192296849351215967318418806142870 340282366820112723708281746854488433920 22300745198070561833654140286697776662304750 1461501637330005217495693490636320631866573150500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 201 64971 16774473 4295000271 1099512556201 281474984086203 72057593910479721 18446744068243777311 4722366482772223442313 1208925819613886614084651

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.34741520.2.
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.ce_bxl$2$(not in LMFDB)