Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 54 x + 1219 x^{2} - 13824 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0443129142907$, $\pm0.254440268732$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.80359488.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52878$ | $4263764652$ | $281450503931562$ | $18446828240506887648$ | $1208925563061167720110398$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $203$ | $65059$ | $16775759$ | $4294986895$ | $1099511394443$ | $281474951391475$ | $72057593321600495$ | $18446744061381968863$ | $4722366482742438301835$ | $1208925819614544132196099$ |
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 4.0.80359488.2. |
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.cc_bux | $2$ | (not in LMFDB) |