Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 4 x + 9 x^{2} - 17 x^{3} + 27 x^{4} - 34 x^{5} + 36 x^{6} - 32 x^{7} + 16 x^{8}$ |
| Frobenius angles: | $\pm0.0564940722828$, $\pm0.213026985589$, $\pm0.484062464562$, $\pm0.632525598194$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.316180889.1 |
| Galois group: | $C_2 \wr S_4$ |
| 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: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2$ | $352$ | $1682$ | $42944$ | $1475342$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $7$ | $2$ | $11$ | $44$ | $70$ | $125$ | $235$ | $425$ | $1002$ |
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 8.0.316180889.1. |
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.e_j_r_bb | $2$ | 4.4.c_ab_ad_ad |