Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x + 1293 x^{2} - 14336 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.120560706820$, $\pm0.193487102895$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.6733584.3 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52438$ | $4259119236$ | $281451515095582$ | $18447139553571928896$ | $1208928845236721888497798$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $201$ | $64987$ | $16775817$ | $4295059375$ | $1099514379561$ | $281475027728107$ | $72057594748629033$ | $18446744080958401759$ | $4722366482907689551497$ | $1208925819614232025698427$ |
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 4.0.6733584.3. |
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.ce_bxt | $2$ | (not in LMFDB) |