Invariants
Base field: | $\F_{2^{10}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 119 x + 5569 x^{2} - 121856 x^{3} + 1048576 x^{4}$ |
Frobenius angles: | $\pm0.0188777145259$, $\pm0.169755303965$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.90316457.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $932171$ | $1096345888691$ | $1152854296835502272$ | $1208924807889028811300003$ | $1267650595158211596630612968091$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $906$ | $1045554$ | $1073679231$ | $1099510707618$ | $1125899902339546$ | $1152921504737736831$ | $1180591620711572514042$ | $1208925819613621562621634$ | $1237940039285313556813752063$ | $1267650600228226224696764135314$ |
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 4.0.90316457.1. |
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.ep_igf | $2$ | (not in LMFDB) |