Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 121 x + 5705 x^{2} - 123904 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0734698624279$, $\pm0.130488439581$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2618993.1 |
Galois group: | $D_{4}$ |
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: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $930257$ | $1096128334899$ | $1152843814048828148$ | $1208924587566587439268227$ | $1267650604462243841032602086297$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $904$ | $1045346$ | $1073669467$ | $1099510507234$ | $1125899910603184$ | $1152921505877075855$ | $1180591620786688110904$ | $1208925819617405935461250$ | $1237940039285474481970806091$ | $1267650600228232210874306919986$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{10}}$.
Endomorphism algebra over $\F_{2^{10}}$The endomorphism algebra of this simple isogeny class is 4.0.2618993.1. |
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 |
---|---|---|
2.1024.er_ill | $2$ | (not in LMFDB) |