Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 3 x + 8 x^{2} - 14 x^{3} + 23 x^{4} - 28 x^{5} + 32 x^{6} - 24 x^{7} + 16 x^{8}$ |
| Frobenius angles: | $\pm0.186703825206$, $\pm0.325077751382$, $\pm0.470431655554$, $\pm0.626573207929$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.404205625.1 |
| Galois group: | $C_2 \wr C_2\wr C_2$ |
| 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: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $11$ | $1639$ | $5819$ | $80311$ | $1528901$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $12$ | $12$ | $20$ | $45$ | $66$ | $133$ | $276$ | $480$ | $1007$ |
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 8.0.404205625.1. |
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.d_i_o_x | $2$ | 4.4.h_ba_cq_fp |