Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 55 x + 1249 x^{2} - 14080 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0267010353124$, $\pm0.243100561557$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.20876009.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52651$ | $4260571571$ | $281432521031104$ | $18446773344930660899$ | $1208925510898320008823451$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $202$ | $65010$ | $16774687$ | $4294974114$ | $1099511347002$ | $281474951668671$ | $72057593273096122$ | $18446744058521171394$ | $4722366482655368945887$ | $1208925819612686586514450$ |
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 4.0.20876009.1. |
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_bwb | $2$ | (not in LMFDB) |