Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 26 x + 181 x^{2} )^{2}$ |
$1 - 52 x + 1038 x^{2} - 9412 x^{3} + 32761 x^{4}$ | |
Frobenius angles: | $\pm0.0828936782352$, $\pm0.0828936782352$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $8$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24336$ | $1052872704$ | $35120842048656$ | $1151865665532002304$ | $37738505921630646287376$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $130$ | $32134$ | $5922826$ | $1073216974$ | $194263776850$ | $35161828130518$ | $6364291006808410$ | $1151936659928854174$ | $208500535106383986466$ | $37738596847623225142054$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=x^6+60x^3+67$
- $y^2=51x^6+143x^5+26x^4+66x^3+26x^2+143x+51$
- $y^2=x^6+180$
- $y^2=92x^6+114x^5+69x^4+16x^3+131x^2+48x+118$
- $y^2=40x^6+170x^4+170x^2+40$
- $y^2=107x^6+51x^5+165x^4+150x^3+165x^2+51x+107$
- $y^2=68x^6+131x^5+130x^4+81x^3+130x^2+131x+68$
- $y^2=69x^6+33x^4+33x^2+69$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The isogeny class factors as 1.181.aba 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$ |
Base change
This is a primitive isogeny class.