Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 - 5 x + 9 x^{2} - 4 x^{3} - 9 x^{4} + 16 x^{5} - 18 x^{6} + 32 x^{7} - 36 x^{8} - 32 x^{9} + 144 x^{10} - 160 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.0344903181050$, $\pm0.119515692218$, $\pm0.191581845605$, $\pm0.355558113752$, $\pm0.646060364906$, $\pm0.930733274074$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.4296772084853824.1 |
| Galois group: | 12T285 |
| Jacobians: | $0$ |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1/2, 1/2, 1/2, 1/2, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $2$ | $616$ | $166814$ | $15736336$ | $1448764262$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $-2$ | $7$ | $14$ | $43$ | $43$ | $145$ | $326$ | $484$ | $1003$ |
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 12.0.4296772084853824.1. |
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.f_j_e_aj_aq_as | $2$ | (not in LMFDB) |