Invariants
| Base field: | $\F_{2^{2}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 6 x + 19 x^{2} - 43 x^{3} + 76 x^{4} - 96 x^{5} + 64 x^{6}$ |
| Frobenius angles: | $\pm0.0919564268332$, $\pm0.268791443494$, $\pm0.539160395357$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.12086967.1 |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $15$ | $4575$ | $252855$ | $16090275$ | $1139454825$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $19$ | $62$ | $247$ | $1084$ | $4168$ | $16064$ | $65143$ | $263681$ | $1052384$ |
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 $\F_{2^{2}}$.
Endomorphism algebra over $\F_{2^{2}}$| The endomorphism algebra of this simple isogeny class is 6.0.12086967.1. |
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 |
|---|---|---|
| 3.4.g_t_br | $2$ | 3.16.c_ad_p |