Properties

Label 2.256.acd_bwp
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:  $1 - 55 x + 1263 x^{2} - 14080 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.118956977279$, $\pm0.211234389458$
Angle rank:  $2$ (numerical)
Number field:  4.0.23384025.1
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
$A(\F_{q^r})$ 52665 4262441775 281471307382260 18447198836580109275 1208928766171822008997875 79228174693768112160069692400 5192296894592880551794848389495685 340282366988556513561458854879558288275 22300745198545789285089851485507158459221340 1461501637330609101829978991236511445807777984375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 202 65038 16776997 4295073178 1099514307652 281475019980943 72057594538333942 18446744077375133458 4722366482872856769517 1208925819614386135498198

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.23384025.1.
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.cd_bwp$2$(not in LMFDB)