Properties

Label 2.256.acc_bux
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:  $1 - 54 x + 1219 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0443129142907$, $\pm0.254440268732$
Angle rank:  $2$ (numerical)
Number field:  4.0.80359488.2
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
$A(\F_{q^r})$ 52878 4263764652 281450503931562 18446828240506887648 1208925563061167720110398 79228155387548799915467493708 5192296806917995883852851282405818 340282366693534699422117091334047686528 22300745197929905484582320228737603219592238 1461501637330800108117488999565028100993253618732

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65059 16775759 4294986895 1099511394443 281474951391475 72057593321600495 18446744061381968863 4722366482742438301835 1208925819614544132196099

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.80359488.2.
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.cc_bux$2$(not in LMFDB)