Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 + 3 x + 7 x^{2} + 21 x^{3} + 43 x^{4} + 65 x^{5} + 129 x^{6} + 189 x^{7} + 189 x^{8} + 243 x^{9} + 243 x^{10}$ |
| Frobenius angles: | $\pm0.301681854727$, $\pm0.415573819332$, $\pm0.464717603270$, $\pm0.844622477384$, $\pm0.888308766885$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.4343523185111747.1 |
| Galois group: | $C_2 \wr S_5$ |
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: | $5$ |
| Slopes: | $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1133$ | $103103$ | $40693961$ | $3249497251$ | $620709881693$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $7$ | $15$ | $55$ | $75$ | $167$ | $807$ | $2093$ | $6771$ | $19063$ | $59695$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
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 10.0.4343523185111747.1. |
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 |
|---|---|---|
| 5.3.ad_h_av_br_acn | $2$ | (not in LMFDB) |