Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 17 x + 138 x^{2} - 685 x^{3} + 2208 x^{4} - 4352 x^{5} + 4096 x^{6}$ |
| Frobenius angles: | $\pm0.102554998327$, $\pm0.191626633307$, $\pm0.385414273973$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.760751703.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 8 |
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: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1389$ | $15969333$ | $69915830319$ | $282217734025173$ | $1153050302391052719$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $244$ | $4167$ | $65708$ | $1048695$ | $16782871$ | $268490922$ | $4295191100$ | $68719697136$ | $1099509812359$ |
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 endomorphism algebra of this simple isogeny class is 6.0.760751703.1. |
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 |
|---|---|---|
| 3.16.r_fi_baj | $2$ | (not in LMFDB) |