Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 9 x + 23 x^{2} )^{2}$ |
$1 - 18 x + 127 x^{2} - 414 x^{3} + 529 x^{4}$ | |
Frobenius angles: | $\pm0.112386341891$, $\pm0.112386341891$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $1$ |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $225$ | $245025$ | $145443600$ | $78218105625$ | $41439153155625$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $6$ | $460$ | $11952$ | $279508$ | $6438306$ | $148061230$ | $3405008382$ | $78312048868$ | $1801158026256$ | $41426535034300$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=21x^6+3x^5+15x^4+18x^3+19x^2+18x+17$
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 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$ |
Base change
This is a primitive isogeny class.