Properties

Label 2.1024.aer_iln
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:  $1 - 121 x + 5707 x^{2} - 123904 x^{3} + 1048576 x^{4}$
Frobenius angles:  $\pm0.0871162508491$, $\pm0.121660722535$
Angle rank:  $2$ (numerical)
Number field:  4.0.4262225.4
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $930259$ $1096132552031$ $1152844593684497956$ $1208924666159945980035659$ $1267650610256271666584353541149$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $904$ $1045350$ $1073670193$ $1099510578714$ $1125899915749314$ $1152921506179822311$ $1180591620802039338796$ $1208925819618095793433074$ $1237940039285502322162675537$ $1267650600228233221590429296950$

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 4.0.4262225.4.

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_iln$2$(not in LMFDB)