Properties

Label 2.256.acc_bvh
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:  $1 - 54 x + 1229 x^{2} - 13824 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0990202301465$, $\pm0.236948812150$
Angle rank:  $2$ (numerical)
Number field:  4.0.6493968.1
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
$A(\F_{q^r})$ 52888 4265099872 281477703607672 18447118933019534208 1208927712388655419997848 79228167566593882462990400608 5192296862101991184803029686264568 340282366896792058517385534650582711808 22300745198548520334644149504297093192184728 1461501637332500392627008186306150046316608328032

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 203 65079 16777379 4295054575 1099513349243 281474994660135 72057594087432275 18446744072400572383 4722366482873435091755 1208925819615950574578199

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.6493968.1.
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_bvh$2$(not in LMFDB)