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

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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.

Point counts of the abelian variety

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

Point counts of the (virtual) curve

$r$ 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:
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.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.
TwistExtension DegreeCommon 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)