Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 7 x + 29 x^{2} - 77 x^{3} + 145 x^{4} - 175 x^{5} + 125 x^{6}$ |
| Frobenius angles: | $\pm0.176517753780$, $\pm0.315873182333$, $\pm0.446146277524$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.3627911.1 |
| Galois group: | $A_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 3 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $41$ | $22919$ | $2595341$ | $254148791$ | $30449662741$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $35$ | $161$ | $651$ | $3119$ | $15767$ | $78616$ | $390803$ | $1952027$ | $9765735$ |
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 6.0.3627911.1. |
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_bd_cz | $2$ | 3.25.j_cb_kv |