Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $1$ |
| L-polynomial: | $1 + 4 x + 5 x^{2}$ |
| Frobenius angles: | $\pm0.852416382350$ |
| Angle rank: | $1$ (numerical) |
| Number field: | \(\Q(\sqrt{-1}) \) |
| Galois group: | $C_2$ |
| Jacobians: | 1 |
This isogeny class is simple and geometrically simple.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $1$ |
| Slopes: | $[0, 1]$ |
Point counts
This isogeny class contains the Jacobians of 1 curves, and hence is principally polarizable:
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $10$ | $20$ | $130$ | $640$ | $3050$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $10$ | $20$ | $130$ | $640$ | $3050$ | $15860$ | $77570$ | $391680$ | $1951690$ | $9766100$ |
Decomposition and endomorphism algebra
Endomorphism algebra over $\F_{5}$| The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1}) \). |
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 |
|---|---|---|
| 1.5.ae | $2$ | 1.25.ag |
| 1.5.ac | $4$ | 1.625.o |
| 1.5.c | $4$ | 1.625.o |