Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 - 3 x + 7 x^{2} - 12 x^{3} + 17 x^{4} - 20 x^{5} + 29 x^{6} - 40 x^{7} + 68 x^{8} - 96 x^{9} + 112 x^{10} - 96 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.133697449860$, $\pm0.184772415084$, $\pm0.396565339023$, $\pm0.486112470475$, $\pm0.571022472996$, $\pm0.811784262314$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.15063571002607033433.1 |
| Galois group: | 12T293 |
| Jacobians: | $0$ |
| Cyclic group of points: | yes |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $31$ | $17515$ | $416299$ | $14800175$ | $1066374611$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $10$ | $9$ | $14$ | $35$ | $121$ | $154$ | $294$ | $567$ | $895$ |
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 12.0.15063571002607033433.1. |
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.d_h_m_r_u_bd | $2$ | (not in LMFDB) |