Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 + x + 2 x^{2} + x^{3} + 5 x^{4} - x^{5} - 2 x^{7} + 20 x^{8} + 8 x^{9} + 32 x^{10} + 32 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.122288410051$, $\pm0.352712914252$, $\pm0.396487740571$, $\pm0.673524735984$, $\pm0.723527324953$, $\pm0.843848571432$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.82246146636020436296.1 |
| Galois group: | 12T293 |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $5$ |
| Slopes: | $[0, 0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $163$ | $13855$ | $177181$ | $50778575$ | $520439603$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $4$ | $8$ | $7$ | $32$ | $9$ | $47$ | $179$ | $352$ | $529$ | $1083$ |
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 $\F_{2}$.
Endomorphism algebra over $\F_{2}$| The endomorphism algebra of this simple isogeny class is 12.0.82246146636020436296.1. |
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_c_ab_f_b_a | $2$ | (not in LMFDB) |