Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 42 x + 701 x^{2} - 5502 x^{3} + 17161 x^{4}$ |
Frobenius angles: | $\pm0.0650836808263$, $\pm0.173182857662$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.194112.5 |
Galois group: | $D_{4}$ |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12319$ | $288350833$ | $5048818516516$ | $86729045036858793$ | $1488382950554161438519$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $90$ | $16800$ | $2245824$ | $294495988$ | $38579643330$ | $5053916090238$ | $662062655178966$ | $86730203714621284$ | $11361656654999045136$ | $1488377021715468367440$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=89x^6+79x^5+113x^4+87x^3+125x^2+36x+10$
- $y^2=37x^6+48x^5+48x^4+130x^3+91x^2+53x+19$
- $y^2=27x^6+84x^5+31x^4+60x^3+17x^2+24x+42$
- $y^2=7x^6+48x^5+16x^4+115x^3+29x^2+46x+83$
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 4.0.194112.5. |
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.bq_baz | $2$ | (not in LMFDB) |