Invariants
| Base field: | $\F_{5}$ |
| Dimension: | $4$ |
| L-polynomial: | $( 1 - 4 x + 5 x^{2} )^{2}( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$ |
| $1 - 11 x + 59 x^{2} - 205 x^{3} + 524 x^{4} - 1025 x^{5} + 1475 x^{6} - 1375 x^{7} + 625 x^{8}$ | |
| Frobenius angles: | $\pm0.147583617650$, $\pm0.147583617650$, $\pm0.235523574971$, $\pm0.521566933142$ |
| Angle rank: | $3$ (numerical) |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.
Newton polygon
This isogeny class is ordinary.
| $p$-rank: | $4$ |
| Slopes: | $[0, 0, 0, 0, 1, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $68$ | $360400$ | $252268916$ | $159798476800$ | $104455895241728$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-5$ | $23$ | $127$ | $655$ | $3410$ | $16391$ | $78731$ | $390495$ | $1954999$ | $9768698$ |
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 2 $\times$ 2.5.ad_j and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
|
Base change
This is a primitive isogeny class.