Invariants
| Base field: | $\F_{3}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 - 5 x + 17 x^{2} - 46 x^{3} + 102 x^{4} - 194 x^{5} + 306 x^{6} - 414 x^{7} + 459 x^{8} - 405 x^{9} + 243 x^{10}$ |
| Frobenius angles: | $\pm0.0374447078939$, $\pm0.259599260360$, $\pm0.391682006333$, $\pm0.558518149638$, $\pm0.626189263211$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.349098857617088.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $64$ | $140288$ | $10019584$ | $2911256576$ | $893599673024$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $19$ | $20$ | $67$ | $259$ | $640$ | $1987$ | $6603$ | $19550$ | $58079$ |
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 10.0.349098857617088.1. |
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.f_r_bu_dy_hm | $2$ | (not in LMFDB) |