Invariants
Base field: | $\F_{23}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 7 x + 23 x^{2} )^{2}$ |
$1 - 14 x + 95 x^{2} - 322 x^{3} + 529 x^{4}$ | |
Frobenius angles: | $\pm0.239612957690$, $\pm0.239612957690$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $2$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $289$ | $277729$ | $151486864$ | $78899753881$ | $41479615178089$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $10$ | $524$ | $12448$ | $281940$ | $6444590$ | $148045358$ | $3404702066$ | $78309903844$ | $1801147929184$ | $41426502960764$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 2 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+14x^5+5x^4+5x^2+14x+8$
- $y^2=17x^6+2x^5+15x^4+11x^2+5x+15$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{23}$.
Endomorphism algebra over $\F_{23}$The isogeny class factors as 1.23.ah 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-43}) \)$)$ |
Base change
This is a primitive isogeny class.