Invariants
| Base field: | $\F_{7}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 10 x + 51 x^{2} - 166 x^{3} + 357 x^{4} - 490 x^{5} + 343 x^{6}$ |
| Frobenius angles: | $\pm0.0683199847700$, $\pm0.284796870547$, $\pm0.407332955184$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.12178624.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 2 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $86$ | $121948$ | $44162978$ | $13762075696$ | $4658150804726$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $52$ | $376$ | $2388$ | $16488$ | $116920$ | $823226$ | $5765724$ | $40354270$ | $282490672$ |
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 $\F_{7}$.
Endomorphism algebra over $\F_{7}$| The endomorphism algebra of this simple isogeny class is 6.0.12178624.1. |
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.k_bz_gk | $2$ | (not in LMFDB) |