Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $1 + 3 x + 8 x^{2} + 14 x^{3} + 25 x^{4} + 34 x^{5} + 53 x^{6} + 68 x^{7} + 100 x^{8} + 112 x^{9} + 128 x^{10} + 96 x^{11} + 64 x^{12}$ |
| Frobenius angles: | $\pm0.225737475123$, $\pm0.416267178839$, $\pm0.511096053293$, $\pm0.646402346767$, $\pm0.779765245285$, $\pm0.812119064030$ |
| Angle rank: | $6$ (numerical) |
| Number field: | 12.0.782394669817139369.1 |
| Galois group: | 12T293 |
| Jacobians: | $2$ |
This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $706$ | $36712$ | $223096$ | $30911504$ | $675522686$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $6$ | $12$ | $6$ | $28$ | $21$ | $96$ | $132$ | $220$ | $483$ | $867$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobians of 2 curves (of which 0 are hyperelliptic):
- $x^{5} + x^{2} y^{3} + x^{4} + x^{3} y + x^{2} y^{2} + y^{4} + x^{2} y + x y^{2} + x y + y=0$
- $ x^{8} + x^{4} y^{4} + x^{5} y + x^{4} y^{2} + x^{3} y^{3} + x^{2} y^{4} + x^{4} y + x^{2} y^{3} + x^{4} + x^{2} y^{2} + x^{2} y + x y^{2} + y^{3} + x y=0$
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 12.0.782394669817139369.1. |
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.ad_i_ao_z_abi_cb | $2$ | (not in LMFDB) |