Properties

Label 2.1024.aer_ilj
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:  $1 - 121 x + 5703 x^{2} - 123904 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0619615785169$, $\pm0.136456221421$
Angle rank:  $2$ (numerical)
Number field:  4.0.47833065.2
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
$A(\F_{q^r})$ 930255 1096124117775 1152843034413295260 1208924508955637761402875 1267650598662766665032730330525 1329227996899447524854802876055383600 1393796574971722509854868493967760624411315 1461501637333415965196006218951502695945153657875 1532495540865970236042861238211996846442790997018490420 1606938044258992501390298621565977612112150250400747826594375

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 904 1045342 1073668741 1099510435738 1125899905452214 1152921505573549087 1180591620771247500796 1208925819616707918456658 1237940039285446011269167789 1267650600228231157381436844502

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.47833065.2.
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.er_ilj$2$(not in LMFDB)