Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 15 x^{2} + 25 x^{3} + 240 x^{4} + 4096 x^{6}$ |
| Frobenius angles: | $\pm0.268440525140$, $\pm0.469255584959$, $\pm0.775495104641$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.979954538135391.1 |
| Galois group: | $S_4\times C_2$ |
| Isomorphism classes: | 912 |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4377$ | $18939279$ | $70005733623$ | $283663524704475$ | $1150862199100780827$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $17$ | $287$ | $4172$ | $66047$ | $1046702$ | $16785068$ | $268432832$ | $4294651127$ | $68719462637$ | $1099512462752$ |
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 6.0.979954538135391.1. |
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.a_p_az | $2$ | (not in LMFDB) |