Invariants
Base field: | $\F_{29}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 10 x + 29 x^{2} )^{2}$ |
$1 - 20 x + 158 x^{2} - 580 x^{3} + 841 x^{4}$ | |
Frobenius angles: | $\pm0.121118941591$, $\pm0.121118941591$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $400$ | $640000$ | $588547600$ | $500131840000$ | $420828298810000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $10$ | $758$ | $24130$ | $707118$ | $20517050$ | $594887078$ | $17250342770$ | $500249228638$ | $14507160605290$ | $420707297939798$ |
Jacobians and polarizations
This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:
- $y^2=8x^6+26x^4+26x^2+8$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{29}$.
Endomorphism algebra over $\F_{29}$The isogeny class factors as 1.29.ak 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$ |
Base change
This is a primitive isogeny class.