Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 7 x + 16 x^{2} )( 1 - 10 x + 49 x^{2} - 160 x^{3} + 256 x^{4} )$ |
| $1 - 17 x + 135 x^{2} - 663 x^{3} + 2160 x^{4} - 4352 x^{5} + 4096 x^{6}$ | |
| Frobenius angles: | $\pm0.0660425289118$, $\pm0.160861246510$, $\pm0.412497962872$ |
| Angle rank: | $3$ (numerical) |
| Isomorphism classes: | 432 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1360$ | $15536640$ | $68444775760$ | $279959936471040$ | $1151407619028994000$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $238$ | $4080$ | $65182$ | $1047200$ | $16782094$ | $268492560$ | $4295137342$ | $68719391040$ | $1099510001198$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$| The isogeny class factors as 1.16.ah $\times$ 2.16.ak_bx and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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 |
|---|---|---|
| 3.16.ad_af_x | $2$ | (not in LMFDB) |
| 3.16.d_af_ax | $2$ | (not in LMFDB) |
| 3.16.r_ff_zn | $2$ | (not in LMFDB) |