Properties

Label 2.256.acd_bwd
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:  $1 - 55 x + 1251 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0468977989438$, $\pm0.239713717685$
Angle rank:  $2$ (numerical)
Number field:  4.0.50319009.1
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
$A(\F_{q^r})$ 52653 4260838719 281438061848100 18446834335464510699 1208925983194026518273403 79228158345531974764319490000 5192296818140332506309041433509553 340282366707193121246268879717245382099 22300745197802058037676408059741817237319900 1461501637329800024955612734633395033476749971359

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65014 16775017 4294988314 1099511776552 281474961900343 72057593477341702 18446744062122393394 4722366482715365551897 1208925819613716882793654

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.50319009.1.
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_bwd$2$(not in LMFDB)