Invariants
Base field: | $\F_{23}$ |
Dimension: | $1$ |
L-polynomial: | $1 - 5 x + 23 x^{2}$ |
Frobenius angles: | $\pm0.325452467839$ |
Angle rank: | $1$ (numerical) |
Number field: | \(\Q(\sqrt{-67}) \) |
Galois group: | $C_2$ |
Jacobians: | $1$ |
Isomorphism classes: | 1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $19$ | $551$ | $12388$ | $280459$ | $6434369$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $19$ | $551$ | $12388$ | $280459$ | $6434369$ | $148011824$ | $3404750543$ | $78311164275$ | $1801155279244$ | $41426520185711$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-67}) \). |
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 |
---|---|---|
1.23.f | $2$ | (not in LMFDB) |