Properties

Label 2.256.acc_buv
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:  $1 - 54 x + 1217 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0252993429206$, $\pm0.257321499971$
Angle rank:  $2$ (numerical)
Number field:  4.0.1991232.3
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
$A(\F_{q^r})$ 52876 4263497632 281445064084300 18446769895982889600 1208925126070961163281356 79228152823968236180655498400 5192296794297266023633725007028236 340282366637667668946656343129134246400 22300745197685864620733368862942618102130700 1461501637329646965326943492871880815540626366112

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65055 16775435 4294973311 1099510997003 281474942283807 72057593146452683 18446744058353411071 4722366482690760638795 1208925819613590274836255

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.1991232.3.
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.cc_buv$2$(not in LMFDB)