Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 57 x + 1294 x^{2} - 13851 x^{3} + 59049 x^{4}$ |
Frobenius angles: | $\pm0.0633476822834$, $\pm0.177798504376$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.749377.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $46436$ | $3447965872$ | $205812638597072$ | $12157631007105115584$ | $717898604376423493652876$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $187$ | $58389$ | $14343436$ | $3486774521$ | $847289337277$ | $205891149605862$ | $50031545341577287$ | $12157665460889020529$ | $2954312706540937526452$ | $717897987691243702749909$ |
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 4.0.749377.1. |
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 |
---|---|---|
2.243.cf_bxu | $2$ | (not in LMFDB) |