Invariants
| Base field: | $\F_{3^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 12 x + 70 x^{2} - 257 x^{3} + 630 x^{4} - 972 x^{5} + 729 x^{6}$ |
| Frobenius angles: | $\pm0.0749946225172$, $\pm0.217193452972$, $\pm0.419068678586$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.62548403.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 6 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $189$ | $504819$ | $398983725$ | $281059492707$ | $205254129344229$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $78$ | $751$ | $6530$ | $58868$ | $532125$ | $4787312$ | $43047730$ | $387372424$ | $3486669078$ |
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 $\F_{3^{2}}$.
Endomorphism algebra over $\F_{3^{2}}$| The endomorphism algebra of this simple isogeny class is 6.0.62548403.1. |
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 |
|---|---|---|
| 3.9.m_cs_jx | $2$ | (not in LMFDB) |