Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $6$ |
| L-polynomial: | $( 1 - x + 2 x^{2} - 3 x^{3} + 4 x^{4} - 4 x^{5} + 8 x^{6} )^{2}$ |
| $1 - 2 x + 5 x^{2} - 10 x^{3} + 18 x^{4} - 28 x^{5} + 49 x^{6} - 56 x^{7} + 72 x^{8} - 80 x^{9} + 80 x^{10} - 64 x^{11} + 64 x^{12}$ | |
| Frobenius angles: | $\pm0.164170413030$, $\pm0.164170413030$, $\pm0.473057015341$, $\pm0.473057015341$, $\pm0.705194715932$, $\pm0.705194715932$ |
| Angle rank: | $3$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $49$ | $25921$ | $117649$ | $21799561$ | $1499006089$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $1$ | $11$ | $1$ | $23$ | $41$ | $101$ | $239$ | $215$ | $415$ | $1181$ |
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 isogeny class factors as 3.2.ab_c_ad 2 and its endomorphism algebra is $\mathrm{M}_{2}($6.0.8140239.1$)$ |
Base change
This is a primitive isogeny class.