# Properties

 Label 2.1024.aev_iuy 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: $( 1 - 32 x )^{2}( 1 - 61 x + 1024 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.0978468837242$ 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 $A(\F_{q^r})$ 926404 1095615396216 1152808632239482204 1208922742163319108750000 1267650522115407331168052142004 1329227993977954773010729652811272616 1393796574871561031163407795909813873305804 1461501637330307533168958172847762755572677500000 1532495540865882803531643447114550576638493827173373604 1606938044258990269014137665954783890189867353245477709261016

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 900 1044856 1073636700 1099508828848 1125899837464500 1152921503039558056 1180591620686407428300 1208925819614136683748448 1237940039285375383849064100 1267650600228229396347157719256

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acm $\times$ 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: 1.1024.acm : the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$. 1.1024.acj : $$\Q(\sqrt{-15})$$.
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.ad_actk $2$ (not in LMFDB) 2.1024.d_actk $2$ (not in LMFDB) 2.1024.ev_iuy $2$ (not in LMFDB) 2.1024.abd_ds $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.ad_actk $2$ (not in LMFDB) 2.1024.d_actk $2$ (not in LMFDB) 2.1024.ev_iuy $2$ (not in LMFDB) 2.1024.abd_ds $3$ (not in LMFDB) 2.1024.acj_dau $4$ (not in LMFDB) 2.1024.cj_dau $4$ (not in LMFDB) 2.1024.adp_fxw $6$ (not in LMFDB) 2.1024.bd_ds $6$ (not in LMFDB) 2.1024.dp_fxw $6$ (not in LMFDB)