# Properties

 Label 2.1024.aet_iqa Base Field $\F_{2^{10}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $( 1 - 32 x )^{2}( 1 - 59 x + 1024 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.126656933887$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

## Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 928326 1095866563176 1152825229127557566 1208923561781703617850000 1267650555391964814215699520246 1329227995113563729488002591815809656 1393796574903069602279749350904453363737966 1461501637330900613437903255218535073537222100000 1532495540865880577829228417381822223222160866054405926 1606938044258989331725334303533374560351395663449303519515016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 902 1045096 1073652158 1099509574288 1125899867020022 1152921504024541816 1180591620713096226158 1208925819614627268248608 1237940039285373585940971302 1267650600228228656956663845256

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acm $\times$ 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: 1.1024.acm : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.1024.ach : $$\Q(\sqrt{-615})$$.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.af_acom $2$ (not in LMFDB) 2.1024.f_acom $2$ (not in LMFDB) 2.1024.et_iqa $2$ (not in LMFDB) 2.1024.abb_ge $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.af_acom $2$ (not in LMFDB) 2.1024.f_acom $2$ (not in LMFDB) 2.1024.et_iqa $2$ (not in LMFDB) 2.1024.abb_ge $3$ (not in LMFDB) 2.1024.ach_dau $4$ (not in LMFDB) 2.1024.ch_dau $4$ (not in LMFDB) 2.1024.adn_fvk $6$ (not in LMFDB) 2.1024.bb_ge $6$ (not in LMFDB) 2.1024.dn_fvk $6$ (not in LMFDB)