Properties

 Label 1.1024.ach Base Field $\F_{2^{10}}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{2^{10}}$ Dimension: $1$ L-polynomial: $1 - 59 x + 1024 x^{2}$ Frobenius angles: $\pm0.126656933887$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-615})$$ Galois group: $C_2$

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 966 1047144 1073717694 1099511671440 1125899934128886 1152921506172025464 1180591620781815702894 1208925819616826291504160 1237940039285443954685148966 1267650600228230908756477530504

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 966 1047144 1073717694 1099511671440 1125899934128886 1152921506172025464 1180591620781815702894 1208925819616826291504160 1237940039285443954685148966 1267650600228230908756477530504

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{10}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-615})$$.
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 1.1024.ch $2$ (not in LMFDB)