Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x + 1281 x^{2} - 14336 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0283703195117$, $\pm0.228136732104$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.12906000.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $52426$ | $4257515460$ | $281417663857066$ | $18446758351864930560$ | $1208925823246027437106666$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $201$ | $64963$ | $16773801$ | $4294970623$ | $1099511631081$ | $281474961280963$ | $72057593441185161$ | $18446744059886787583$ | $4722366482638581299721$ | $1208925819611852852240323$ |
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 4.0.12906000.2. |
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.ce_bxh | $2$ | (not in LMFDB) |