Properties

Label 2.1024.aet_iqb
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:  $1 - 123 x + 5825 x^{2} - 125952 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0257138497233$, $\pm0.123950606712$
Angle rank:  $2$ (numerical)
Number field:  4.0.6943545.3
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
$A(\F_{q^r})$ 928327 1095868671979 1152825625390443376 1208923602703473942554355 1267650558510662829835012783327 1329227995309955670707109622094992576 1393796574913881146022344592084490066511407 1461501637331438092823749357834982650227544994595 1532495540865905207768525277438960148902221440608357616 1606938044258990386745785105504204688429631251651199596789179

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 902 1045098 1073652527 1099509611506 1125899869789982 1152921504194884671 1180591620722253959918 1208925819615071860776226 1237940039285393481847489583 1267650600228229489221051691578

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.6943545.3.
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.et_iqb$2$(not in LMFDB)