Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 + 3 x + 9 x^{2} + 16 x^{3} + 40 x^{4} + 64 x^{5} + 120 x^{6} + 144 x^{7} + 243 x^{8} + 243 x^{9} + 243 x^{10}$ |
| Frobenius angles: | $\pm0.269739630828$, $\pm0.396596663634$, $\pm0.630736681512$, $\pm0.741952506742$, $\pm0.774234463085$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.22304667352595456.1 |
| Galois group: | $C_2 \wr S_5$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1126$ | $209436$ | $11030296$ | $6334182384$ | $723214476266$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $7$ | $19$ | $22$ | $131$ | $207$ | $664$ | $2247$ | $6427$ | $19840$ | $58359$ |
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 10.0.22304667352595456.1. |
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_j_aq_bo_acm | $2$ | (not in LMFDB) |