Invariants
Base field: | $\F_{3^{5}}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 56 x + 1265 x^{2} - 13608 x^{3} + 59049 x^{4}$ |
Frobenius angles: | $\pm0.0783982229649$, $\pm0.190397219869$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.445225.1 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $46651$ | $3451194329$ | $205834903662784$ | $12157739442976229641$ | $717899010627359245105091$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $188$ | $58444$ | $14344988$ | $3486805620$ | $847289816748$ | $205891155303238$ | $50031545391647700$ | $12157665461262443684$ | $2954312706548675193764$ | $717897987691553646133564$ |
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 4.0.445225.1. |
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.ce_bwr | $2$ | (not in LMFDB) |