Properties

Label 2.1024.aeq_iix
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:  $( 1 - 63 x + 1024 x^{2} )( 1 - 57 x + 1024 x^{2} )$
Frobenius angles:  $\pm0.0563432964760$, $\pm0.150267280813$
Angle rank:  $2$ (numerical)

This isogeny class is not 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
$A(\F_{q^r})$ 931216 1096242374656 1152849996118925104 1208924787902243336331264 1267650606031793288026545428176 1329227996937475653166295557364770816 1393796574961795566447621668617760484179056 1461501637332633392849077637618121722829985972224 1532495540865929758892457863589398992476473178068594704 1606938044258990816661176912609456593530688303408756796286976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045455 1073675225 1099510689439 1125899911997225 1152921505606533231 1180591620762839052665 1208925819616060589783359 1237940039285413314087463625 1267650600228229828364496840975

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acl $\times$ 1.1024.acf and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ag_achj$2$(not in LMFDB)
2.1024.g_achj$2$(not in LMFDB)
2.1024.eq_iix$2$(not in LMFDB)