Properties

Label 2.1024.aer_ilj
Base field $\F_{2^{10}}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{2^{10}}$
Dimension:  $2$
L-polynomial:  $1 - 121 x + 5703 x^{2} - 123904 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0619615785169$, $\pm0.136456221421$
Angle rank:  $2$ (numerical)
Number field:  4.0.47833065.2
Galois group:  $D_{4}$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $930255$ $1096124117775$ $1152843034413295260$ $1208924508955637761402875$ $1267650598662766665032730330525$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $904$ $1045342$ $1073668741$ $1099510435738$ $1125899905452214$ $1152921505573549087$ $1180591620771247500796$ $1208925819616707918456658$ $1237940039285446011269167789$ $1267650600228231157381436844502$

Jacobians and polarizations

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

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{10}}$.

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.47833065.2.

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.er_ilj$2$(not in LMFDB)