Invariants
| Base field: | $\F_{2^{4}}$ |
| Dimension: | $3$ |
| L-polynomial: | $( 1 - 4 x )^{4}( 1 - 5 x + 16 x^{2} )$ |
| $1 - 21 x + 192 x^{2} - 992 x^{3} + 3072 x^{4} - 5376 x^{5} + 4096 x^{6}$ | |
| Frobenius angles: | $0$, $0$, $0$, $0$, $\pm0.285098958592$ |
| Angle rank: | $1$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
| $p$-rank: | $1$ |
| Slopes: | $[0, 1/2, 1/2, 1/2, 1/2, 1]$ |
Point counts
Point counts of the abelian variety
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $972$ | $13365000$ | $66351471732$ | $279064541250000$ | $1148945823878496732$ |
Point counts of the (virtual) curve
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $-4$ | $200$ | $3956$ | $64976$ | $1044956$ | $16755800$ | $268337156$ | $4294621856$ | $68718535916$ | $1099509305000$ |
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 $\F_{2^{4}}$.
Endomorphism algebra over $\F_{2^{4}}$The isogeny class factors as 1.16.ai 2 $\times$ 1.16.af 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.