Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 4 x + 10 x^{2} - 19 x^{3} + 30 x^{4} - 36 x^{5} + 27 x^{6}$ |
| Frobenius angles: | $\pm0.125412673718$, $\pm0.335294135736$, $\pm0.584823404300$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.11822771.1 |
| Galois group: | $S_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 2 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9$ | $1143$ | $18981$ | $545211$ | $15988419$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $14$ | $27$ | $82$ | $270$ | $713$ | $2142$ | $6898$ | $20412$ | $59174$ |
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 6.0.11822771.1. |
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.e_k_t | $2$ | 3.9.e_i_f |