Properties

Label 2.1024.aeo_idv
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:  $1 - 118 x + 5507 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0313213001784$, $\pm0.177453654500$
Angle rank:  $2$ (numerical)
Number field:  4.0.350965824.1
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
$A(\F_{q^r})$ 933134 1096464176556 1152861323107998122 1208925102290755603946976 1267650604500750112493321354174 1329227996153023289638660607137591884 1393796574904290663979727965159046376032954 1461501637329690607455489656291931623951315443584 1532495540865807571973064744986549579667972163319725742 1606938044258986527115808091085534170542722135925854031295276

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045667 1073685775 1099510975375 1125899910637387 1152921504926129267 1180591620714130505647 1208925819613626374758879 1237940039285314612280012875 1267650600228226444509854205827

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.350965824.1.
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_idv$2$(not in LMFDB)