Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 4 x + 5 x^{2} )^{3}$ |
| $1 - 12 x + 63 x^{2} - 184 x^{3} + 315 x^{4} - 300 x^{5} + 125 x^{6}$ | |
| Frobenius angles: | $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.147583617650$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $0$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $3$ |
| Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $8$ | $8000$ | $1815848$ | $262144000$ | $32829478408$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-6$ | $8$ | $114$ | $668$ | $3354$ | $16328$ | $79794$ | $393788$ | $1957434$ | $9767048$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but does not contain a Jacobian.
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{5}$.
Endomorphism algebra over $\F_{5}$| The isogeny class factors as 1.5.ae 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-1}) \)$)$ |
Base change
This is a primitive isogeny class.