Properties

Label 2.1024.aeq_iit
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:  $1 - 120 x + 5635 x^{2} - 122880 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0353584911826$, $\pm0.156761072952$
Angle rank:  $2$ (numerical)
Number field:  4.0.865449.1
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
$A(\F_{q^r})$ 931212 1096233940944 1152848449738917972 1208924633741416941278016 1267650594817829263530587225052 1329227996271732814921497326521304784 1393796574927716166142114602187880145098532 1461501637331082390995712731976761842656771360000 1532495540865865852342850107934864993028171155903957292 1606938044258988406592707524341273338530598704726931664602704

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 905 1045447 1073673785 1099510549231 1125899902037225 1152921505029093367 1180591620733972677785 1208925819614777631120223 1237940039285361690787804745 1267650600228227927155702434727

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.865449.1.
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.eq_iit$2$(not in LMFDB)