Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 - x + 2 x^{2} - 3 x^{3} + 5 x^{4} - 8 x^{5} + 10 x^{6} - 12 x^{7} + 16 x^{8} - 16 x^{9} + 32 x^{10}$ |
| Frobenius angles: | $\pm0.0994169633814$, $\pm0.302205847474$, $\pm0.467227201178$, $\pm0.662419229126$, $\pm0.792324369619$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.43964889247231488.1 |
| Galois group: | $C_2 \wr S_5$ |
| Jacobians: | $1$ |
| Cyclic group of points: | yes |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
| $p$-rank: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1/2, 1/2, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $26$ | $2756$ | $20072$ | $1609504$ | $25170106$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $2$ | $8$ | $5$ | $24$ | $22$ | $65$ | $142$ | $256$ | $545$ | $1148$ |
Jacobians and polarizations
This isogeny class is principally polarizable and contains the Jacobian of 1 curve (which is not hyperelliptic):
- $x t + y^2 + y z + z^2 + z t = x^2 + x u + y z + y u + z t + z u + t^2 + t u + u^2 = x^2 + x z + y^2 + y u + t u + u^2 = 0$
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 10.0.43964889247231488.1. |
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 |
|---|---|---|
| 5.2.b_c_d_f_i | $2$ | (not in LMFDB) |