Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 - 3 x + 7 x^{2} - 14 x^{3} + 24 x^{4} - 38 x^{5} + 48 x^{6} - 56 x^{7} + 56 x^{8} - 48 x^{9} + 32 x^{10}$ |
| Frobenius angles: | $\pm0.0412480727610$, $\pm0.282003169751$, $\pm0.402232452313$, $\pm0.603836419769$, $\pm0.683622363228$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.12634026150128.1 |
| Galois group: | $C_2 \wr S_5$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 8 |
This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $2$ |
| Slopes: | $[0, 0, 1/3, 1/3, 1/3, 2/3, 2/3, 2/3, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9$ | $2943$ | $10476$ | $1168371$ | $29888829$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $0$ | $10$ | $3$ | $18$ | $30$ | $19$ | $112$ | $274$ | $453$ | $990$ |
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 10.0.12634026150128.1. |
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.d_h_o_y_bm | $2$ | (not in LMFDB) |