Invariants
| Base field: | $\F_{7}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 10 x + 50 x^{2} - 161 x^{3} + 350 x^{4} - 490 x^{5} + 343 x^{6}$ |
| Frobenius angles: | $\pm0.0597053245252$, $\pm0.252383275250$, $\pm0.434095383219$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.24504179.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 2 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $83$ | $116615$ | $42378887$ | $13607221275$ | $4691372514113$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $50$ | $361$ | $2362$ | $16608$ | $117545$ | $823534$ | $5760082$ | $40334572$ | $282471750$ |
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 6.0.24504179.1. |
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_by_gf | $2$ | (not in LMFDB) |