Properties

Label 2.1024.aep_igt
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:  $1 - 119 x + 5583 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0838690408520$, $\pm0.147968261758$
Angle rank:  $2$ (numerical)
Number field:  4.0.100858905.2
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
$A(\F_{q^r})$ 932185 1096375404975 1152859664049922420 1208925336491899853494875 1267650632982698175656594386675 1329227998133598069518230666885724400 1393796575010701267419041697552539607365605 1461501637334490711755911569058888800677655529875 1532495540865995321236935852049709416525850099971048540 1606938044258992953352200417308664640425951787166499766824375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045582 1073684229 1099511188378 1125899935934436 1152921506644004047 1180591620804263792694 1208925819617596927974418 1237940039285466274927566861 1267650600228231513916511820502

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.100858905.2.
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.ep_igt$2$(not in LMFDB)