Properties

Label 2.256.acf_byt
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:  $1 - 57 x + 1319 x^{2} - 14592 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0877663768024$, $\pm0.194516460330$
Angle rank:  $2$ (numerical)
Number field:  4.0.11282985.3
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
$A(\F_{q^r})$ 52207 4255131535 281417620395100 18446921754861614715 1208927676529502458073437 79228171475517950254211038000 5192296888430667753621823298444947 340282366987134841623310914325361609235 22300745198583462726848339350794906148486900 1461501637330748333027591315391913359785395978375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 200 64926 16773797 4295008666 1099513316630 281475008547423 72057594452816060 18446744077298064466 4722366482880834431117 1208925819614501304845526

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.11282985.3.
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.cf_byt$2$(not in LMFDB)