Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $4$ |
| L-polynomial: | $1 - 2 x + 4 x^{3} - 6 x^{4} + 8 x^{5} - 16 x^{7} + 16 x^{8}$ |
| Frobenius angles: | $\pm0.133582184824$, $\pm0.190415260312$, $\pm0.513309389920$, $\pm0.956476314431$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 8.0.214798336.3 |
| Galois group: | $S_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 2 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular.
Newton polygon
| $p$-rank: | $0$ |
| Slopes: | $[1/4, 1/4, 1/4, 1/4, 3/4, 3/4, 3/4, 3/4]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $5$ | $85$ | $8765$ | $37825$ | $2524525$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $1$ | $13$ | $9$ | $61$ | $97$ | $169$ | $241$ | $553$ | $1041$ |
Jacobians and polarizations
This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.
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 8.0.214798336.3. |
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.c_a_ae_ag | $2$ | 4.4.ae_e_q_aci |
| 4.2.ac_e_ai_k | $4$ | (not in LMFDB) |
| 4.2.c_e_i_k | $4$ | (not in LMFDB) |