Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 11 x + 61 x^{2} - 222 x^{3} + 579 x^{4} - 1110 x^{5} + 1525 x^{6} - 1375 x^{7} + 625 x^{8}$ |
| Frobenius angles: | $\pm0.0374067743831$, $\pm0.206112897288$, $\pm0.309896481618$, $\pm0.465991063903$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.2071948309.1 |
| Galois group: | $C_2 \wr S_4$ |
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: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $73$ | $402157$ | $276998281$ | $149496636709$ | $93676590558953$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-5$ | $27$ | $142$ | $615$ | $3070$ | $15594$ | $77744$ | $388423$ | $1949155$ | $9766042$ |
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 8.0.2071948309.1. |
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 |
|---|---|---|
| 4.5.l_cj_io_wh | $2$ | (not in LMFDB) |