Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x + 1264 x^{2} - 13608 x^{3} + 59049 x^{4}$ |
Frobenius angles: | $\pm0.0688954693548$, $\pm0.194232931048$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.8241408.2 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $46650$ | $3451073700$ | $205832490712650$ | $12157713339645450000$ | $717898808972201175068250$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $188$ | $58442$ | $14344820$ | $3486798134$ | $847289578748$ | $205891149290714$ | $50031545265036404$ | $12157665458998586846$ | $2954312706514463772380$ | $717897987691133634107882$ |
Jacobians and polarizations
This isogeny class contains a Jacobian, and hence is principally polarizable.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{3^{5}}$.
Endomorphism algebra over $\F_{3^{5}}$The endomorphism algebra of this simple isogeny class is 4.0.8241408.2. |
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 |
---|---|---|
2.243.ce_bwq | $2$ | (not in LMFDB) |