Properties

Label 2.1024.aeo_ied
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 118 x + 5515 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0632249866452$, $\pm0.168323205285$
Angle rank:  $2$ (numerical)
Number field:  4.0.521407040.1
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
$A(\F_{q^r})$ 933142 1096481041964 1152864364306391506 1208925398297769669476960 1267650625364487596259491725702 1329227997343457338723808938609812236 1393796574962343212156305252608751468838242 1461501637332183606761829831363460481767374227840 1532495540865903522158167219540915505573041270568357686 1606938044258989873779154562440114395741872241598626061461804

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045683 1073688607 1099511244591 1125899929168107 1152921505958666211 1180591620763302926623 1208925819615688535452191 1237940039285392120222285963 1267650600228229084561731173203

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.521407040.1.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.eo_ied$2$(not in LMFDB)