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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 926404 1095615396216 1152808632239482204 1208922742163319108750000 1267650522115407331168052142004 1329227993977954773010729652811272616 1393796574871561031163407795909813873305804 1461501637330307533168958172847762755572677500000 1532495540865882803531643447114550576638493827173373604 1606938044258990269014137665954783890189867353245477709261016

Point counts of the (virtual) curve

$r$ 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:
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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)