Properties

Label 2.256.acc_bvb
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:  $1 - 54 x + 1223 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0693907236630$, $\pm0.248166754731$
Angle rank:  $2$ (numerical)
Number field:  4.0.1551424.1
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
$A(\F_{q^r})$ 52882 4264298716 281461383713902 18446944723532711136 1208926429916870251244962 79228160386857313210216654684 5192296830571602563222885933826238 340282366789955236222451958566189299584 22300745198295987784834695475716994399282162 1461501637332271044413943804064567641365866990876

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65067 16776407 4295014015 1099512182843 281474969152587 72057593649860231 18446744066608936639 4722366482819959244267 1208925819615760862182827

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1551424.1.
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.cc_bvb$2$(not in LMFDB)