Properties

Label 2.256.acj_cdl
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:  $1 - 61 x + 1441 x^{2} - 15616 x^{3} + 65536 x^{4}$
Frobenius angles:  $\pm0.0492306350850$, $\pm0.129653471103$
Angle rank:  $2$ (numerical)
Number field:  4.0.97625.1
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
$A(\F_{q^r})$ 51301 4240284155 281305144678996 18446318368618006355 1208925205185227318292541 79228164090379574766197209280 5192296877457507729941155469231341 340282367026441959893160996097997555555 22300745198977035365295431583396183139205716 1461501637332424590962235192915131290332224296875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 196 64698 16767091 4294868178 1099511068956 281474982310143 72057594300532876 18446744079428907618 4722366482964176679091 1208925819615887872910698

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{8}}$
The endomorphism algebra of this simple isogeny class is 4.0.97625.1.
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.cj_cdl$2$(not in LMFDB)