Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x + 1289 x^{2} - 14336 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0929357896899$, $\pm0.208872909793$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.2816912.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52434$ | $4258584612$ | $281440231225794$ | $18447012761006965248$ | $1208927847757902306575634$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $201$ | $64979$ | $16775145$ | $4295029855$ | $1099513472361$ | $281475006234995$ | $72057594346244169$ | $18446744075262544063$ | $4722366482861567420169$ | $1208925819614660125492499$ |
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 4.0.2816912.1. |
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.ce_bxp | $2$ | (not in LMFDB) |