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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 931222 1096255025284 1152852315689950942 1208925019011549193079616 1267650622812206964641990380102 1329227997929465546513369165381139364 1393796575012146795949019551274033770960462 1461501637334889083646166945959159951552126240000 1532495540866020099211223452435452861485836018008891382 1606938044258994054606389051407781903310116914248593961230404

Point counts of the curve

$r$ 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.
TwistExtension DegreeCommon base change
2.1024.eq_ijd$2$(not in LMFDB)