Properties

Label 2.1024.aes_int
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:  $( 1 - 63 x + 1024 x^{2} )( 1 - 59 x + 1024 x^{2} )$
Frobenius angles:  $\pm0.0563432964760$, $\pm0.126656933887$
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
$A(\F_{q^r})$ 929292 1095999550464 1152834919429745916 1208924116004855258910720 1267650583102074686927394015852 1329227996383476994338591747854201856 1393796574957776044717124815165979149673052 1461501637333149353218500005063461780956095201280 1532495540865969630193605329261363581399316569347920076 1606938044258992751308492065777860505623735069053558804091904

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 903 1045223 1073661183 1099510078351 1125899891631543 1152921505126015991 1180591620759434385327 1208925819616487382197791 1237940039285445521868036327 1267650600228231354532129156103

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acl $\times$ 1.1024.ach 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.ae_acmf$2$(not in LMFDB)
2.1024.e_acmf$2$(not in LMFDB)
2.1024.es_int$2$(not in LMFDB)