# Properties

 Label 2.1024.aeq_ijd 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: $1 - 120 x + 5645 x^{2} - 122880 x^{3} + 1048576 x^{4}$ Frobenius angles: $\pm0.0849929122078$, $\pm0.135745716650$ Angle rank: $2$ (numerical) Number field: 4.0.28778256.1 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 $A(\F_{q^r})$ 931222 1096255025284 1152852315689950942 1208925019011549193079616 1267650622812206964641990380102 1329227997929465546513369165381139364 1393796575012146795949019551274033770960462 1461501637334889083646166945959159951552126240000 1532495540866020099211223452435452861485836018008891382 1606938044258994054606389051407781903310116914248593961230404

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 905 1045467 1073677385 1099510899631 1125899926901225 1152921506466947307 1180591620805488202985 1208925819617926453478623 1237940039285486290415798345 1267650600228232382652887944827

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is 4.0.28778256.1.
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_ijd $2$ (not in LMFDB)