Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 131 x^{2} )( 1 - 19 x + 131 x^{2} )$ |
$1 - 40 x + 661 x^{2} - 5240 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.130292526609$, $\pm0.188329584469$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $9$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12543$ | $289780929$ | $5053017790800$ | $86738097300847929$ | $1488398865585321524703$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $92$ | $16884$ | $2247692$ | $294526724$ | $38580055852$ | $5053920750918$ | $662062699214932$ | $86730204040523524$ | $11361656656338089972$ | $1488377021704362582804$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=82x^6+91x^5+118x^4+125x^3+68x^2+21x+70$
- $y^2=74x^6+118x^5+98x^4+89x^3+119x^2+47x+107$
- $y^2=125x^6+32x^5+51x^4+x^3+50x^2+78x+3$
- $y^2=76x^6+42x^5+119x^4+117x^3+92x^2+67x+79$
- $y^2=20x^6+2x^5+113x^4+30x^3+46x^2+26x+107$
- $y^2=107x^6+93x^5+13x^4+29x^3+62x^2+86x+5$
- $y^2=110x^6+99x^5+72x^4+85x^3+93x^2+114x+69$
- $y^2=40x^6+104x^5+10x^4+84x^3+14x^2+120x+115$
- $y^2=54x^6+76x^5+59x^4+53x^3+48x^2+92x+115$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{131}$.
Endomorphism algebra over $\F_{131}$The isogeny class factors as 1.131.av $\times$ 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.ac_afh | $2$ | (not in LMFDB) |
2.131.c_afh | $2$ | (not in LMFDB) |
2.131.bo_zl | $2$ | (not in LMFDB) |