Invariants
| Base field: | $\F_{2}$ |
| Dimension: | $5$ |
| L-polynomial: | $1 - 5 x + 14 x^{2} - 29 x^{3} + 50 x^{4} - 75 x^{5} + 100 x^{6} - 116 x^{7} + 112 x^{8} - 80 x^{9} + 32 x^{10}$ |
| Frobenius angles: | $\pm0.0882933931853$, $\pm0.191709583463$, $\pm0.338081491767$, $\pm0.491435615996$, $\pm0.678554723993$ |
| Angle rank: | $5$ (numerical) |
| Number field: | 10.0.2869065680951.1 |
| Galois group: | $C_2 \wr S_5$ |
| Jacobians: | $0$ |
| Isomorphism classes: | 2 |
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: | $5$ |
| Slopes: | $[0, 0, 0, 0, 0, 1, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $4$ | $2456$ | $25084$ | $1262384$ | $42126004$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-2$ | $8$ | $7$ | $20$ | $38$ | $65$ | $159$ | $268$ | $511$ | $1158$ |
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 10.0.2869065680951.1. |
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.f_o_bd_by_cx | $2$ | (not in LMFDB) |