Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 60 x + 1409 x^{2} - 15360 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0412211280464$, $\pm0.155266595880$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.553104.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $51526$ | $4243990516$ | $281333081669494$ | $18446463967581198144$ | $1208925740119460597608726$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $197$ | $64755$ | $16768757$ | $4294902079$ | $1099511555477$ | $281474985568371$ | $72057594223947557$ | $18446744075553808639$ | $4722366482858991730277$ | $1208925819613668169775475$ |
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 4.0.553104.2. |
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.ci_ccf | $2$ | (not in LMFDB) |