Invariants
| Base field: | $\F_{131}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 41 x + 681 x^{2} - 5371 x^{3} + 17161 x^{4}$ |
| Frobenius angles: | $\pm0.106655216392$, $\pm0.178582845263$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.210125.1 |
| Galois group: | $C_4$ |
| 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $12431$ | $289082905$ | $5051059775441$ | $86734197603598205$ | $1488392909012132054416$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $91$ | $16843$ | $2246821$ | $294513483$ | $38579901456$ | $5053919441023$ | $662062694276431$ | $86730204127404963$ | $11361656658899196061$ | $1488377021746752168198$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=82x^6+122x^5+51x^4+71x^3+105x^2+24x+69$
- $y^2=61x^6+104x^5+65x^4+41x^3+79x^2+6x+2$
- $y^2=90x^6+129x^5+86x^4+62x^3+96x^2+105x+128$
- $y^2=96x^6+67x^5+117x^4+75x^3+116x^2+44x+57$
- $y^2=14x^6+89x^5+11x^4+130x^3+8x^2+66x+71$
- $y^2=43x^6+111x^5+84x^4+66x^3+77x^2+71x+39$
- $y^2=86x^6+114x^5+111x^4+32x^3+16x^2+18x+50$
- $y^2=16x^6+76x^5+12x^4+73x^3+52x^2+53x+122$
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 4.0.210125.1. |
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.bp_baf | $2$ | (not in LMFDB) |