Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 18 x + 153 x^{2} - 775 x^{3} + 2448 x^{4} - 4608 x^{5} + 4096 x^{6}$ |
| Frobenius angles: | $\pm0.0553436146881$, $\pm0.250233467979$, $\pm0.311381340818$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.17734383.1 |
| Galois group: | $A_4\times C_2$ |
| Isomorphism classes: | 4 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1297$ | $15692403$ | $70479380773$ | $283564876383003$ | $1152655576178040397$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $239$ | $4202$ | $66023$ | $1048334$ | $16765556$ | $268373132$ | $4294809095$ | $68719531823$ | $1099513958084$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$| The endomorphism algebra of this simple isogeny class is 6.0.17734383.1. |
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.s_fx_bdv | $2$ | (not in LMFDB) |