Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6}$ |
| Frobenius angles: | $\pm0.0749012311065$, $\pm0.225515375241$, $\pm0.553262127050$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.29215664.1 |
| Galois group: | $S_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $29$ | $14819$ | $1730372$ | $235814747$ | $31945643129$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $25$ | $110$ | $605$ | $3269$ | $15832$ | $77517$ | $389701$ | $1954586$ | $9765045$ |
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 $\F_{5}$.
Endomorphism algebra over $\F_{5}$| The endomorphism algebra of this simple isogeny class is 6.0.29215664.1. |
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 |
|---|---|---|
| 3.5.h_y_ch | $2$ | 3.25.ab_ak_db |