# 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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 930259 1096132552031 1152844593684497956 1208924666159945980035659 1267650610256271666584353541149 1329227997598432964211643213586638736 1393796575008075095786549535608547830029999 1461501637335093803089395423249777599924159183699 1532495540866039945552582417648566889167970772699599036 1606938044258995118086066900423193806052094667431399654039951

 $r$ 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.
 Twist Extension Degree Common base change 2.1024.er_iln $2$ (not in LMFDB)