Properties

Label 2.1024.aeo_ief
Base Field $\F_{2^{10}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 118 x + 5517 x^{2} - 120832 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0698761161827$, $\pm0.165566469990$
Angle rank:  $2$ (numerical)
Number field:  4.0.28299024.1
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 933144 1096485258336 1152865124606320632 1208925472255545143389056 1267650630567136359416052230424 1329227997638938987557167461072547424 1393796574976615814094254062853484729725304 1461501637332785302489335105611683204920644427264 1532495540865925883965330995281375335872155186043468312 1606938044258990603403275465564646945521034187872102838567776

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 907 1045687 1073689315 1099511311855 1125899933788987 1152921506214955687 1180591620775392290707 1208925819616186246492639 1237940039285410183946258155 1267650600228229660133675659927

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.28299024.1.
All geometric endomorphisms are defined over $\F_{2^{10}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.1024.eo_ief$2$(not in LMFDB)