Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 + x - x^{2} - 3 x^{4} - 3 x^{5} + 7 x^{6} - 6 x^{7} - 12 x^{8} - 16 x^{10} + 32 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.0430884721787$, $\pm0.248079428433$, $\pm0.477259307350$, $\pm0.568025754910$, $\pm0.868962538268$, $\pm0.983187046962$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 12.0.144869678261310016.1 |
| Galois group: | $S_6\times C_2$ |
| Jacobians: | $0$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $6$ |
| Slopes: | $[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $64$ | $1024$ | $446464$ | $4489216$ | $1512147904$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $4$ | $2$ | $13$ | $-2$ | $44$ | $71$ | $88$ | $190$ | $481$ | $1002$ |
Jacobians and polarizations
This isogeny class is not principally polarizable, and therefore does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2}$.
Endomorphism algebra over $\F_{2}$| The endomorphism algebra of this simple isogeny class is 12.0.144869678261310016.1. |
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 |
|---|---|---|
| 6.2.ab_ab_a_ad_d_h | $2$ | (not in LMFDB) |