Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 - x + 2 x^{2} - x^{3} - 3 x^{4} + 5 x^{5} - 15 x^{6} + 10 x^{7} - 12 x^{8} - 8 x^{9} + 32 x^{10} - 32 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.0312435366809$, $\pm0.287325614314$, $\pm0.417669060044$, $\pm0.527172365216$, $\pm0.644672686383$, $\pm0.961401725286$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.3156290330218484615217.1 |
| Galois group: | 12T293 |
| Jacobians: | $0$ |
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: | $6$ |
| Slopes: | $[0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $42$ | $4032$ | $246078$ | $5330304$ | $1190954982$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $8$ | $11$ | $0$ | $37$ | $29$ | $114$ | $216$ | $479$ | $1003$ |
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 12.0.3156290330218484615217.1. |
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.b_c_b_ad_af_ap | $2$ | (not in LMFDB) |