Invariants
| Base field: | $\F_{131}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 19 x + 131 x^{2} )^{2}$ |
| $1 - 38 x + 623 x^{2} - 4978 x^{3} + 17161 x^{4}$ | |
| Frobenius angles: | $\pm0.188329584469$, $\pm0.188329584469$ |
| Angle rank: | $1$ (numerical) |
| Jacobians: | $7$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $12769$ | $291145969$ | $5056651690000$ | $86744647524460249$ | $1488406824690880065409$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $94$ | $16964$ | $2249308$ | $294548964$ | $38580262154$ | $5053921397318$ | $662062677510734$ | $86730203444447044$ | $11361656646688293028$ | $1488377021587554390404$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 7 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=111x^6+21x^5+33x^4+105x^3+16x^2+20x+98$
- $y^2=72x^6+121x^5+7x^4+6x^3+63x^2+129x+110$
- $y^2=56x^6+30x^5+18x^4+107x^3+12x^2+x+102$
- $y^2=122x^6+30x^5+87x^4+2x^3+43x^2+3x+23$
- $y^2=6x^6+45x^5+71x^4+17x^3+82x^2+63x+70$
- $y^2=14x^6+7x^5+53x^4+29x^3+2x^2+28x+17$
- $y^2=98x^6+90x^5+127x^4+96x^3+127x^2+90x+98$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$| The isogeny class factors as 1.131.at 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-163}) \)$)$ |
Base change
This is a primitive isogeny class.