Properties

Label 2.1024.aep_ign
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:  $1 - 119 x + 5577 x^{2} - 121856 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0603251282655$, $\pm0.159355937826$
Angle rank:  $2$ (numerical)
Number field:  4.0.3429225.3
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
$A(\F_{q^r})$ 932179 1096362755091 1152857363814367936 1208925110053359410237379 1267650616804359600913435073899 1329227997196895351241603583176343296 1393796574964398044257401147572085529006579 1461501637332485175379344827498183235678204326979 1532495540865918449115749170039582055215314811008408256 1606938044258990358332138384290913015993757098462013893012451

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 906 1045570 1073682087 1099510982434 1125899921565186 1152921505831543951 1180591620765043437114 1208925819615937987165954 1237940039285404178122594743 1267650600228229466806636618450

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.3429225.3.
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.ep_ign$2$(not in LMFDB)