Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $3$ |
| L-polynomial: | $1 + 3 x^{2} + x^{3} + 6 x^{4} + 8 x^{6}$ |
| Frobenius angles: | $\pm0.317790270383$, $\pm0.460816543721$, $\pm0.731339684822$ |
| Angle rank: | $3$ (numerical) |
| Number field: | 6.0.1305639.1 |
| Galois group: | $A_4\times C_2$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 1 |
| 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: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $19$ | $323$ | $703$ | $5491$ | $21869$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $3$ | $11$ | $12$ | $23$ | $18$ | $56$ | $150$ | $215$ | $525$ | $1136$ |
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 6.0.1305639.1. |
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 |
|---|---|---|
| 3.2.a_d_ab | $2$ | 3.4.g_v_bz |