Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 131 x^{2} )( 1 - 18 x + 131 x^{2} )$ |
$1 - 39 x + 640 x^{2} - 5109 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.130292526609$, $\pm0.211976702993$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $21$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12654$ | $290409300$ | $5054442442056$ | $86739851650471200$ | $1488398852121016833954$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $93$ | $16921$ | $2248326$ | $294532681$ | $38580055503$ | $5053919578018$ | $662062674021933$ | $86730203712894481$ | $11361656653753329666$ | $1488377021704632064201$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=43x^6+77x^4+88x^3+99x^2+20x+112$
- $y^2=50x^6+17x^5+45x^4+77x^3+22x^2+99x+130$
- $y^2=20x^6+64x^5+85x^4+96x^3+6x^2+108x+47$
- $y^2=x^6+43x^5+97x^4+93x^3+73x^2+124x+109$
- $y^2=7x^6+118x^5+10x^4+104x^3+90x^2+58x+8$
- $y^2=26x^6+111x^5+110x^4+59x^3+74x^2+85x+20$
- $y^2=103x^6+29x^5+68x^4+86x^3+79x^2+88x+102$
- $y^2=31x^6+16x^5+47x^4+70x^3+4x^2+109x+64$
- $y^2=72x^6+31x^5+60x^4+33x^3+130x^2+116x+78$
- $y^2=73x^6+130x^5+97x^4+21x^3+111x^2+123x+89$
- $y^2=21x^6+84x^5+98x^4+107x^3+40x^2+9x+90$
- $y^2=119x^6+62x^5+67x^4+103x^3+35x^2+27x+119$
- $y^2=71x^6+84x^5+104x^4+8x^3+52x^2+12x+32$
- $y^2=111x^6+5x^5+75x^4+114x^3+108x^2+93x+81$
- $y^2=6x^6+82x^5+38x^4+36x^3+67x^2+107x+26$
- $y^2=43x^6+127x^5+104x^4+76x^3+63x^2+66x+111$
- $y^2=69x^6+119x^5+128x^4+29x^3+114x^2+2x+42$
- $y^2=78x^6+76x^5+51x^4+111x^3+125x^2+28x+78$
- $y^2=14x^6+25x^5+68x^4+100x^3+8x^2+97x+29$
- $y^2=19x^6+115x^5+13x^4+78x^3+42x^2+67x+24$
- $y^2=15x^6+44x^5+23x^4+74x^3+55x^2+92x+13$
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.as 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_aem | $2$ | (not in LMFDB) |
2.131.d_aem | $2$ | (not in LMFDB) |
2.131.bn_yq | $2$ | (not in LMFDB) |