Properties

Label 2.1024.aeq_ijf
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:  $( 1 - 61 x + 1024 x^{2} )( 1 - 59 x + 1024 x^{2} )$
Frobenius angles:  $\pm0.0978468837242$, $\pm0.126656933887$
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
$A(\F_{q^r})$ 931224 1096259242176 1152853088880563784 1208925096012802153440000 1267650628394869560858818592504 1329227998258362789945865479917950656 1393796575028725963933473618634891128374184 1461501637335622140386326174655911852207136640000 1532495540866048747574388368621732015032446269192616024 1606938044258995034188280700995824119473061965357890382990016

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045471 1073678105 1099510969663 1125899931859625 1152921506752220191 1180591620819531304505 1208925819618532823801983 1237940039285509432379266505 1267650600228233155406745729631

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The isogeny class factors as 1.1024.acj $\times$ 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.ac_achr$2$(not in LMFDB)
2.1024.c_achr$2$(not in LMFDB)
2.1024.eq_ijf$2$(not in LMFDB)