Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 131 x^{2} )( 1 - 17 x + 131 x^{2} )$ |
$1 - 38 x + 619 x^{2} - 4978 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.130292526609$, $\pm0.233569366159$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $36$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12765$ | $291003705$ | $5055624408240$ | $86740769024833545$ | $1488397060905536929125$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $94$ | $16956$ | $2248852$ | $294535796$ | $38580009074$ | $5053917994758$ | $662062650235094$ | $86730203513313316$ | $11361656653816434412$ | $1488377021738310500076$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=79x^6+78x^5+15x^4+92x^3+15x^2+78x+79$
- $y^2=82x^6+61x^5+9x^4+91x^3+9x^2+61x+82$
- $y^2=110x^6+100x^4+62x^3+100x^2+110$
- $y^2=55x^6+76x^5+123x^4+121x^3+3x^2+48x+104$
- $y^2=72x^6+125x^5+31x^4+15x^3+116x^2+97x+73$
- $y^2=74x^6+98x^5+95x^4+73x^3+110x^2+57x+65$
- $y^2=88x^6+11x^5+20x^4+75x^3+36x^2+118x+32$
- $y^2=127x^6+23x^5+96x^4+68x^3+65x^2+119x+51$
- $y^2=10x^6+21x^5+85x^4+127x^3+85x^2+21x+10$
- $y^2=110x^6+7x^5+83x^4+79x^3+97x^2+74x+67$
- $y^2=90x^6+118x^5+88x^4+71x^3+88x^2+118x+90$
- $y^2=93x^6+125x^5+54x^4+37x^3+54x^2+125x+93$
- $y^2=111x^6+51x^5+74x^4+122x^3+69x^2+106x+124$
- $y^2=70x^6+27x^5+126x^4+83x^3+24x^2+105x+94$
- $y^2=78x^6+18x^5+91x^4+103x^3+20x^2+75x+76$
- $y^2=31x^6+77x^5+107x^4+99x^3+107x^2+77x+31$
- $y^2=98x^6+81x^5+103x^4+46x^3+103x^2+81x+98$
- $y^2=76x^6+105x^5+13x^4+70x^3+13x^2+105x+76$
- $y^2=54x^6+71x^5+116x^4+79x^3+71x^2+6x+37$
- $y^2=56x^6+78x^5+72x^4+87x^3+118x^2+73x+6$
- and 16 more
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.ar 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.ae_adr | $2$ | (not in LMFDB) |
2.131.e_adr | $2$ | (not in LMFDB) |
2.131.bm_xv | $2$ | (not in LMFDB) |