Properties

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

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 118 x + 5505 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0178869819368$, $\pm0.179404760049$
Angle rank:  $2$ (numerical)
Number field:  4.0.8700480.3
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
$A(\F_{q^r})$ 933132 1096459960224 1152860562808730316 1208925028245024039803520 1267650599271530133712274072652 1329227995853287360526763189642577056 1393796574889536757788903509185948965544332 1461501637329045751682574853612674492637439470080 1532495540865781950675416397932589070159910640020456076 1606938044258985582438461611178362913885124411105026383507104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045663 1073685067 1099510908031 1125899905992907 1152921504666149791 1180591620701633461003 1208925819613092962565631 1237940039285293915560595723 1267650600228225699290827519903

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.8700480.3.
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_idt$2$(not in LMFDB)