Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 5 x + 15 x^{2} - 31 x^{3} + 45 x^{4} - 45 x^{5} + 27 x^{6}$ |
| Frobenius angles: | $\pm0.113296540390$, $\pm0.351823865540$, $\pm0.481790494592$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.400967.1 |
| Galois group: | $A_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $7$ | $1183$ | $26173$ | $445991$ | $13038697$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $15$ | $35$ | $67$ | $219$ | $759$ | $2288$ | $6707$ | $20069$ | $59875$ |
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 6.0.400967.1. |
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 |
|---|---|---|
| 3.3.f_p_bf | $2$ | 3.9.f_f_ah |