Invariants
Base field: | $\F_{2^{4}}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 4 x )^{2}( 1 - 10 x + 51 x^{2} - 160 x^{3} + 256 x^{4} )$ |
$1 - 18 x + 147 x^{2} - 728 x^{3} + 2352 x^{4} - 4608 x^{5} + 4096 x^{6}$ | |
Frobenius angles: | $0$, $0$, $\pm0.118775077357$, $\pm0.396715540983$ |
Angle rank: | $2$ (numerical) |
This isogeny class is not simple, primitive, not ordinary, and not supersingular. It is principally polarizable.
Newton polygon
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1/2, 1/2, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $1242$ | $14841900$ | $67410885150$ | $278530575717600$ | $1149080543839229562$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $227$ | $4019$ | $64847$ | $1045079$ | $16771091$ | $268456019$ | $4295077727$ | $68719349399$ | $1099509187427$ |
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 $\times$ 2.16.ak_bz 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.