Properties

 Label 1.512.abt Base Field $\F_{2^{9}}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

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Invariants

 Base field: $\F_{2^{9}}$ Dimension: $1$ L-polynomial: $1 - 45 x + 512 x^{2}$ Frobenius angles: $\pm0.0337960018969$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-23})$$ 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 $A(\F_{q^r})$ 468 261144 134195724 68718999024 35184361858308 18014398293697416 9223372032382499004 4722366482778874456800 2417851639227463471076148 1237940039285345980001526264

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 468 261144 134195724 68718999024 35184361858308 18014398293697416 9223372032382499004 4722366482778874456800 2417851639227463471076148 1237940039285345980001526264

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{9}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-23})$$.
All geometric endomorphisms are defined over $\F_{2^{9}}$.

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 1.512.bt $2$ (not in LMFDB)