Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 2 x + 3 x^{2} - 5 x^{3} + 6 x^{4} - 8 x^{5} + 8 x^{6}$ |
| Frobenius angles: | $\pm0.0964297006873$, $\pm0.413303350042$, $\pm0.672715745192$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.3194271.1 |
| Galois group: | $S_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $3$ | $99$ | $243$ | $4059$ | $26763$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $7$ | $4$ | $15$ | $26$ | $52$ | $176$ | $311$ | $481$ | $1072$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$| The endomorphism algebra of this simple isogeny class is 6.0.3194271.1. |
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 |
|---|---|---|
| 3.2.c_d_f | $2$ | 3.4.c_b_af |