Invariants
Base field: | $\F_{2^{9}}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 23 x + 512 x^{2}$ |
Frobenius angles: | $\pm0.330298876614$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-31}) \) |
Galois group: | $C_2$ |
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: | $1$ |
Slopes: | $[0, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $490$ | $262640$ | $134240890$ | $68719756000$ | $35184366653450$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $490$ | $262640$ | $134240890$ | $68719756000$ | $35184366653450$ | $18014398241485520$ | $9223372033473773210$ | $4722366482929096344000$ | $2417851639232356798740010$ | $1237940039285421100254945200$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{9}}$.
Endomorphism algebra over $\F_{2^{9}}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-31}) \). |
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.x | $2$ | (not in LMFDB) |