Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 55 x + 1231 x^{2} - 13365 x^{3} + 59049 x^{4}$ |
Frobenius angles: | $\pm0.0458457648609$, $\pm0.218011583258$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.194725.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $46861$ | $3453702561$ | $205842995957119$ | $12157699099249617021$ | $717898312965197954478736$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $189$ | $58487$ | $14345553$ | $3486794051$ | $847288993344$ | $205891129736243$ | $50031544823774703$ | $12157665451383812243$ | $2954312706413425248399$ | $717897987690201609874022$ |
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 4.0.194725.1. |
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_bvj | $2$ | (not in LMFDB) |