Invariants
| Base field: | $\F_{131}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 40 x + 656 x^{2} - 5240 x^{3} + 17161 x^{4}$ |
| Frobenius angles: | $\pm0.0626218735454$, $\pm0.221898581110$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.2490624.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $8$ |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $12538$ | $289602724$ | $5051665832650$ | $86732551031010064$ | $1488382893526619437978$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $92$ | $16874$ | $2247092$ | $294507894$ | $38579641852$ | $5053913705018$ | $662062603421332$ | $86730203022704734$ | $11361656649036648572$ | $1488377021701807865354$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=30x^6+115x^4+64x^3+8x^2+29x+58$
- $y^2=119x^6+44x^5+58x^4+42x^3+64x^2+9x+67$
- $y^2=98x^6+100x^5+108x^4+15x^3+56x^2+51x+110$
- $y^2=74x^6+112x^5+97x^4+96x^3+74x^2+123x+71$
- $y^2=93x^6+73x^5+127x^4+11x^3+82x^2+72x+113$
- $y^2=98x^6+8x^5+129x^4+120x^3+101x^2+101x+32$
- $y^2=80x^6+60x^5+104x^4+2x^3+112x^2+47x+14$
- $y^2=19x^6+38x^5+124x^4+103x^3+119x^2+105x+24$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$| The endomorphism algebra of this simple isogeny class is 4.0.2490624.2. |
Base change
This is a primitive isogeny class.
Twists
Below is a list of all twists of this isogeny class.
| Twist | Extension degree | Common base change |
|---|---|---|
| 2.131.bo_zg | $2$ | (not in LMFDB) |