Invariants
Base field: | $\F_{23}$ |
Dimension: | $3$ |
L-polynomial: | $( 1 - 5 x + 23 x^{2} )( 1 - 9 x + 23 x^{2} )^{2}$ |
$1 - 23 x + 240 x^{2} - 1463 x^{3} + 5520 x^{4} - 12167 x^{5} + 12167 x^{6}$ | |
Frobenius angles: | $\pm0.112386341891$, $\pm0.112386341891$, $\pm0.325452467839$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $4275$ | $135008775$ | $1801755316800$ | $21936971685481875$ | $266634802450805675625$ |
Point counts of the (virtual) curve
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $1$ | $481$ | $12172$ | $280125$ | $6436331$ | $148037164$ | $3404933477$ | $78312227861$ | $1801160644036$ | $41426544006361$ |
Jacobians and polarizations
This isogeny class is principally polarizable, but it is unknown whether it contains 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.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.