Invariants
Base field: | $\F_{2^{8}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 58 x + 1345 x^{2} - 14848 x^{3} + 65536 x^{4}$ |
Frobenius angles: | $\pm0.0329768133648$, $\pm0.195159409513$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.237632.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $51976$ | $4251013088$ | $281380604689864$ | $18446663247467944832$ | $1208926115449815756054856$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $199$ | $64863$ | $16771591$ | $4294948479$ | $1099511896839$ | $281474978262879$ | $72057593855364295$ | $18446744066261410815$ | $4722366482688615290695$ | $1208925819611334757173343$ |
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 4.0.237632.1. |
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.cg_bzt | $2$ | (not in LMFDB) |