Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 + 2 x + 5 x^{2} + 6 x^{3} + 11 x^{4} + 12 x^{5} + 20 x^{6} + 16 x^{7} + 16 x^{8}$ |
| Frobenius angles: | $\pm0.284109330992$, $\pm0.520934539747$, $\pm0.659718070509$, $\pm0.788797001508$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.4964356096.1 |
| Galois group: | $C_2 \wr C_2\wr C_2$ |
| Jacobians: | $0$ |
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: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $89$ | $1513$ | $2492$ | $110449$ | $1138399$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $5$ | $11$ | $5$ | $27$ | $35$ | $65$ | $103$ | $211$ | $545$ | $1091$ |
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 8.0.4964356096.1. |
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 |
|---|---|---|
| 4.2.ac_f_ag_l | $2$ | 4.4.g_x_co_fp |