Invariants
| Base field: | $\F_{7}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 10 x + 52 x^{2} - 169 x^{3} + 364 x^{4} - 490 x^{5} + 343 x^{6}$ |
| Frobenius angles: | $\pm0.138002645708$, $\pm0.274328089770$, $\pm0.392516251949$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.4770787.1 |
| Galois group: | $A_4\times C_2$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $91$ | $130039$ | $47095867$ | $14364237979$ | $4744758184621$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $54$ | $397$ | $2490$ | $16798$ | $117633$ | $824864$ | $5769762$ | $40360276$ | $282478194$ |
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 6.0.4770787.1. |
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_ca_gn | $2$ | (not in LMFDB) |