# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 931212 1096233940944 1152848449738917972 1208924633741416941278016 1267650594817829263530587225052 1329227996271732814921497326521304784 1393796574927716166142114602187880145098532 1461501637331082390995712731976761842656771360000 1532495540865865852342850107934864993028171155903957292 1606938044258988406592707524341273338530598704726931664602704

 $r$ 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.
 Twist Extension Degree Common base change 2.1024.eq_iit $2$ (not in LMFDB)