Properties

Label 2.256.acd_bwb
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:  $1 - 55 x + 1249 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0267010353124$, $\pm0.243100561557$
Angle rank:  $2$ (numerical)
Number field:  4.0.20876009.1
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
$A(\F_{q^r})$ 52651 4260571571 281432521031104 18446773344930660899 1208925510898320008823451 79228155465572346498856752896 5192296803422887482161809341609691 340282366640762300689315650529640367299 22300745197518732076376248135644482776982464 1461501637328554473181830681726676088040334231251

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65010 16774687 4294974114 1099511347002 281474951668671 72057593273096122 18446744058521171394 4722366482655368945887 1208925819612686586514450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.20876009.1.
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_bwb$2$(not in LMFDB)