Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 55 x + 1251 x^{2} - 14080 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0468977989438$, $\pm0.239713717685$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.50319009.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52653$ | $4260838719$ | $281438061848100$ | $18446834335464510699$ | $1208925983194026518273403$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $202$ | $65014$ | $16775017$ | $4294988314$ | $1099511776552$ | $281474961900343$ | $72057593477341702$ | $18446744062122393394$ | $4722366482715365551897$ | $1208925819613716882793654$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{2^{8}}$.
Endomorphism algebra over $\F_{2^{8}}$The endomorphism algebra of this simple isogeny class is 4.0.50319009.1. |
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 |
---|---|---|
2.256.cd_bwd | $2$ | (not in LMFDB) |