Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 55 x + 1237 x^{2} - 13365 x^{3} + 59049 x^{4}$ |
Frobenius angles: | $\pm0.0952562388508$, $\pm0.200242037068$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.12537189.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $46867$ | $3454425969$ | $205857214491469$ | $12157848981824922861$ | $717899431388356490831632$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $189$ | $58499$ | $14346543$ | $3486837035$ | $847290313344$ | $205891161629903$ | $50031545458805253$ | $12157665461975823299$ | $2954312706560418502059$ | $717897987691833854419814$ |
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 4.0.12537189.1. |
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.cd_bvp | $2$ | (not in LMFDB) |