Invariants
| Base field: | $\F_{7}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 4 x + 22 x^{2} - 55 x^{3} + 154 x^{4} - 196 x^{5} + 343 x^{6}$ |
| Frobenius angles: | $\pm0.257614113219$, $\pm0.456182695828$, $\pm0.522709866441$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.320654347.1 |
| Galois group: | $A_4\times C_2$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $265$ | $205375$ | $44873245$ | $13375046875$ | $4772252090575$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $4$ | $78$ | $379$ | $2322$ | $16894$ | $118641$ | $822686$ | $5753874$ | $40342348$ | $282515118$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains no Jacobian of a hyperelliptic curve, but it is unknown whether it contains a Jacobian of a non-hyperelliptic curve.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{7}$.
Endomorphism algebra over $\F_{7}$| The endomorphism algebra of this simple isogeny class is 6.0.320654347.1. |
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 |
|---|---|---|
| 3.7.e_w_cd | $2$ | (not in LMFDB) |