Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 8 x + 23 x^{2} )^{2}$ |
$1 - 16 x + 110 x^{2} - 368 x^{3} + 529 x^{4}$ | |
Frobenius angles: | $\pm0.186011988595$, $\pm0.186011988595$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $3$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $256$ | $262144$ | $149035264$ | $78722891776$ | $41490294159616$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $8$ | $494$ | $12248$ | $281310$ | $6446248$ | $148081358$ | $3404961400$ | $78311027134$ | $1801149869384$ | $41426487914414$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 3 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=6x^6+10x^5+x^4+21x^3+x^2+10x+6$
- $y^2=4x^6+11x^4+11x^2+4$
- $y^2=14x^6+7x^4+7x^2+14$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.ai 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-7}) \)$)$ |
Base change
This is a primitive isogeny class.