Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 - x + 3 x^{2} - x^{3} + 2 x^{4} + 8 x^{5} - 6 x^{6} + 16 x^{7} + 8 x^{8} - 8 x^{9} + 48 x^{10} - 32 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.163712411094$, $\pm0.266613952028$, $\pm0.401115849757$, $\pm0.575823472753$, $\pm0.593009196599$, $\pm0.919248159814$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.2498903384004718848.1 |
| Galois group: | 12T293 |
| Jacobians: | $0$ |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1/3, 1/3, 1/3, 2/3, 2/3, 2/3, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $102$ | $14076$ | $524178$ | $16271856$ | $2496584742$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $10$ | $14$ | $14$ | $62$ | $70$ | $100$ | $318$ | $518$ | $910$ |
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 12.0.2498903384004718848.1. |
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_d_b_c_ai_ag | $2$ | (not in LMFDB) |