Properties

Label 2.1024.aer_iln
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:  $1 - 121 x + 5707 x^{2} - 123904 x^{3} + 1048576 x^{4}$
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.

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
$A(\F_{q^r})$ 930259 1096132552031 1152844593684497956 1208924666159945980035659 1267650610256271666584353541149 1329227997598432964211643213586638736 1393796575008075095786549535608547830029999 1461501637335093803089395423249777599924159183699 1532495540866039945552582417648566889167970772699599036 1606938044258995118086066900423193806052094667431399654039951

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

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
The endomorphism algebra of this simple isogeny class is 4.0.4262225.4.
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.er_iln$2$(not in LMFDB)