Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 55 x + 1267 x^{2} - 14080 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.147664473873$, $\pm0.191492242764$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1681025.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52669$ | $4262976191$ | $281482389468964$ | $18447319787591103275$ | $1208929674480074430953179$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $202$ | $65046$ | $16777657$ | $4295101338$ | $1099515133752$ | $281475038082711$ | $72057594829782022$ | $18446744080082750898$ | $4722366482851242991177$ | $1208925819612669435564406$ |
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 4.0.1681025.1. |
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_bwt | $2$ | (not in LMFDB) |