# Properties

 Label 2.1024.aey_jci Base Field $\F_{2^{10}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

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## Invariants

 Base field: $\F_{2^{10}}$ Dimension: $2$ L-polynomial: $( 1 - 32 x )^{4}$ Frobenius angles: $0$, $0$, $0$, $0$ Angle rank: $0$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is supersingular.

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

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 923521 1095222947841 1152780773560811521 1208921207935207812890625 1267650449112508705067363205121 1329227990833155722679814984029962241 1393796574745904669523852578373111612702721 1461501637325586006220552422779585474791812890625 1532495540865714633786483514084656171531874968765726721 1606938044258984566551191268509244272979694567707627896176641

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 897 1044481 1073610753 1099507433473 1125899772624897 1152921500311879681 1180591620579972349953 1208925819610231128195073 1237940039285239537410768897 1267650600228224897897075834881

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The isogeny class factors as 1.1024.acm 2 and its endomorphism algebra is $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $2$ and $\infty$.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{2^{10}}$.

 Subfield Primitive Model $\F_{2}$ 2.2.a_ae

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.a_adau $2$ (not in LMFDB) 2.1024.ey_jci $2$ (not in LMFDB) 2.1024.abg_a $3$ (not in LMFDB) 2.1024.cm_eoe $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.1024.a_adau $2$ (not in LMFDB) 2.1024.ey_jci $2$ (not in LMFDB) 2.1024.abg_a $3$ (not in LMFDB) 2.1024.cm_eoe $3$ (not in LMFDB) 2.1024.acm_dau $4$ (not in LMFDB) 2.1024.a_dau $4$ (not in LMFDB) 2.1024.cm_dau $4$ (not in LMFDB) 2.1024.bg_bnk $5$ (not in LMFDB) 2.1024.ads_gbo $6$ (not in LMFDB) 2.1024.acm_eoe $6$ (not in LMFDB) 2.1024.a_bnk $6$ (not in LMFDB) 2.1024.bg_a $6$ (not in LMFDB) 2.1024.ds_gbo $6$ (not in LMFDB) 2.1024.a_a $8$ (not in LMFDB) 2.1024.abg_bnk $10$ (not in LMFDB) 2.1024.abg_dau $12$ (not in LMFDB) 2.1024.a_abnk $12$ (not in LMFDB) 2.1024.bg_dau $12$ (not in LMFDB)