Invariants
Base field: | $\F_{131}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 22 x + 131 x^{2} )( 1 - 16 x + 131 x^{2} )$ |
$1 - 38 x + 614 x^{2} - 4978 x^{3} + 17161 x^{4}$ | |
Frobenius angles: | $\pm0.0891048534084$, $\pm0.253645088345$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $52$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $12760$ | $290825920$ | $5054340389560$ | $86735894461511680$ | $1488384526350771379000$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $94$ | $16946$ | $2248282$ | $294519246$ | $38579684174$ | $5053913323778$ | $662062602219434$ | $86730203247614686$ | $11361656655666643582$ | $1488377021813115675026$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 52 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=42x^6+31x^5+88x^4+18x^3+88x^2+31x+42$
- $y^2=32x^6+88x^5+24x^4+99x^3+45x^2+67x+24$
- $y^2=85x^6+36x^5+130x^4+36x^3+96x^2+16x+37$
- $y^2=31x^6+83x^5+70x^4+2x^3+98x^2+86x+45$
- $y^2=37x^6+4x^5+63x^4+108x^3+91x^2+80x+40$
- $y^2=85x^6+53x^5+35x^4+114x^3+35x^2+53x+85$
- $y^2=112x^6+118x^5+83x^4+14x^3+92x^2+68x+42$
- $y^2=46x^6+56x^5+30x^4+62x^3+35x^2+104x+87$
- $y^2=69x^6+60x^5+104x^4+126x^3+80x^2+106x+5$
- $y^2=6x^6+116x^5+81x^4+42x^3+27x^2+51x+84$
- $y^2=10x^6+55x^5+90x^4+102x^3+15x^2+51x+37$
- $y^2=30x^6+90x^5+100x^4+62x^3+100x^2+90x+30$
- $y^2=42x^6+20x^5+2x^4+52x^3+50x^2+79x+112$
- $y^2=8x^6+4x^5+23x^4+58x^3+4x^2+116$
- $y^2=128x^6+115x^5+77x^4+45x^3+110x^2+20x+2$
- $y^2=51x^6+127x^5+12x^4+68x^3+34x^2+31x+54$
- $y^2=2x^6+9x^5+119x^4+85x^3+28x^2+68x+15$
- $y^2=10x^6+78x^5+18x^4+52x^3+50x^2+70x+128$
- $y^2=101x^6+52x^5+7x^4+48x^3+123x^2+100x+112$
- $y^2=95x^6+75x^5+119x^4+31x^3+25x^2+77x+58$
- and 32 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.aw $\times$ 1.131.aq 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.ag_adm | $2$ | (not in LMFDB) |
2.131.g_adm | $2$ | (not in LMFDB) |
2.131.bm_xq | $2$ | (not in LMFDB) |