Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 54 x + 1223 x^{2} - 13824 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0693907236630$, $\pm0.248166754731$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1551424.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52882$ | $4264298716$ | $281461383713902$ | $18446944723532711136$ | $1208926429916870251244962$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $203$ | $65067$ | $16776407$ | $4295014015$ | $1099512182843$ | $281474969152587$ | $72057593649860231$ | $18446744066608936639$ | $4722366482819959244267$ | $1208925819615760862182827$ |
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 4.0.1551424.1. |
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.cc_bvb | $2$ | (not in LMFDB) |