Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 - x + 9 x^{2} - 9 x^{3} + 39 x^{4} - 37 x^{5} + 117 x^{6} - 81 x^{7} + 243 x^{8} - 81 x^{9} + 243 x^{10}$ |
| Frobenius angles: | $\pm0.217939461989$, $\pm0.422017682783$, $\pm0.472467981864$, $\pm0.564517065583$, $\pm0.710270671194$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.7608027501108819.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $443$ | $381423$ | $14348327$ | $3141781251$ | $877822707743$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $3$ | $27$ | $27$ | $75$ | $253$ | $795$ | $2327$ | $6307$ | $19161$ | $58827$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains 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 10.0.7608027501108819.1. |
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.b_j_j_bn_bl | $2$ | (not in LMFDB) |