Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 7 x - 263 x^{2} - 7168 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.200650491102$, $\pm0.746121712270$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.257829142746329.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1041139$ | $1098910761971$ | $1152892117450101952$ | $1208929999208247374861891$ | $1267650625706570067327888470299$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $1018$ | $1048002$ | $1073714455$ | $1099515429090$ | $1125899929471938$ | $1152921506171740527$ | $1180591620790264404298$ | $1208925819611726954751234$ | $1237940039285366608327427335$ | $1267650600228227423848061150002$ |
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 4.0.257829142746329.1. |
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.h_akd | $2$ | (not in LMFDB) |