Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 22 x + 131 x^{2} )( 1 - 19 x + 131 x^{2} )$ |
$1 - 41 x + 680 x^{2} - 5371 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.0891048534084$, $\pm0.188329584469$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $4$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12430$ | $289047220$ | $5050782583000$ | $86733018815877280$ | $1488389342104374993250$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $91$ | $16841$ | $2246698$ | $294509481$ | $38579809001$ | $5053917758978$ | $662062669209851$ | $86730203821865041$ | $11361656656042065838$ | $1488377021732268347801$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=40x^6+84x^5+101x^4+63x^3+71x^2+24x+128$
- $y^2=3x^6+49x^5+15x^4+23x^3+24x^2+25x+16$
- $y^2=27x^6+111x^5+64x^4+102x^3+6x^2+99x+79$
- $y^2=92x^6+96x^5+114x^4+74x^3+97x^2+105x+38$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The isogeny class factors as 1.131.aw $\times$ 1.131.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ad_aga | $2$ | (not in LMFDB) |
2.131.d_aga | $2$ | (not in LMFDB) |
2.131.bp_bae | $2$ | (not in LMFDB) |