Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 3 x + 7 x^{2} - 12 x^{3} + 19 x^{4} - 24 x^{5} + 28 x^{6} - 24 x^{7} + 16 x^{8}$ |
| Frobenius angles: | $\pm0.152866543232$, $\pm0.297609806907$, $\pm0.480381455271$, $\pm0.659965926501$ |
| Angle rank: | $4$ (numerical) |
| Number field: | 8.0.3339178657.1 |
| Galois group: | $C_2 \wr S_4$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8$ | $1072$ | $3992$ | $87904$ | $1620648$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $10$ | $9$ | $22$ | $45$ | $67$ | $147$ | $262$ | $486$ | $1155$ |
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 8.0.3339178657.1. |
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_h_m_t | $2$ | 4.4.f_p_bi_cn |