Properties

Label 2.1024.aeu_isp
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:  $( 1 - 63 x + 1024 x^{2} )( 1 - 61 x + 1024 x^{2} )$
Frobenius angles:  $\pm0.0563432964760$, $\pm0.0978468837242$
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
$A(\F_{q^r})$ 927368 1095748353024 1152818322402162104 1208923296386095001088000 1267650549825516476473396268648 1329227995247868036776384634415266816 1393796574926267473599546550408166388980888 1461501637332556272949554010149617462405855232000 1532495540865971855896020359123426120248784657947077704 1606938044258993688597295428201264397117765331367992245115904

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 901 1044983 1073645725 1099509332911 1125899862076021 1152921504141032231 1180591620732745587469 1208925819615996797697631 1237940039285447319776129125 1267650600228232093922623030103

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acl $\times$ 1.1024.acj 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.ac_acrb$2$(not in LMFDB)
2.1024.c_acrb$2$(not in LMFDB)
2.1024.eu_isp$2$(not in LMFDB)