Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 - 18 x + 153 x^{2} - 773 x^{3} + 2448 x^{4} - 4608 x^{5} + 4096 x^{6}$ |
| Frobenius angles: | $\pm0.109406132665$, $\pm0.208302636123$, $\pm0.327763380346$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.53163783.1 |
| Galois group: | $A_4\times C_2$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $1299$ | $15714003$ | $70610588649$ | $284197314082827$ | $1154536315694943789$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-1$ | $239$ | $4208$ | $66167$ | $1050044$ | $16778732$ | $268444322$ | $4295072039$ | $68720034011$ | $1099512956564$ |
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 6.0.53163783.1. |
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_bdt | $2$ | (not in LMFDB) |