Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - x + 3 x^{2} - 6 x^{3} + 2 x^{4} - 18 x^{5} + 27 x^{6} - 27 x^{7} + 81 x^{8}$ |
| Frobenius angles: | $\pm0.0782059514466$, $\pm0.439377436916$, $\pm0.531209420686$, $\pm0.781097371409$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.1415573168512.1 |
| Galois group: | $C_2 \wr S_4$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 8 |
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: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $62$ | $10292$ | $393824$ | $32028704$ | $2828489042$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $3$ | $15$ | $18$ | $59$ | $193$ | $822$ | $2243$ | $6387$ | $20070$ | $59135$ |
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 8.0.1415573168512.1. |
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 |
|---|---|---|
| 4.3.b_d_g_c | $2$ | (not in LMFDB) |