Invariants
Base field: | $\F_{23}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 7 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$1 - 25 x + 276 x^{2} - 1717 x^{3} + 6348 x^{4} - 13225 x^{5} + 12167 x^{6}$ | |
Frobenius angles: | $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.239612957690$ |
Angle rank: | $2$ (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: | $3$ |
Slopes: | $[0, 0, 0, 1, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $3825$ | $129128175$ | $1790119828800$ | $21970761907111875$ | $266887498406748676875$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $-1$ | $457$ | $12092$ | $280557$ | $6442429$ | $148065964$ | $3404946691$ | $78311508149$ | $1801155660116$ | $41426530907857$ |
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 $\F_{23}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.aj 2 $\times$ 1.23.ah 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.