Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 4 x + 10 x^{2} - 21 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6}$ |
| Frobenius angles: | $\pm0.0145064862012$, $\pm0.383559653096$, $\pm0.564732805964$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 6.0.309123.1 |
| Galois group: | $D_{6}$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7$ | $903$ | $14539$ | $358491$ | $12358717$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $14$ | $21$ | $50$ | $210$ | $665$ | $2058$ | $6578$ | $19740$ | $57974$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{3}$.
Endomorphism algebra over $\F_{3}$| The endomorphism algebra of this simple isogeny class is 6.0.309123.1. |
Base change
This is a primitive isogeny class.