# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 931224 1096259242176 1152853088880563784 1208925096012802153440000 1267650628394869560858818592504 1329227998258362789945865479917950656 1393796575028725963933473618634891128374184 1461501637335622140386326174655911852207136640000 1532495540866048747574388368621732015032446269192616024 1606938044258995034188280700995824119473061965357890382990016

 $r$ 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.
 Twist Extension Degree Common 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)