Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 23 x + 181 x^{2} )^{2}$ |
$1 - 46 x + 891 x^{2} - 8326 x^{3} + 32761 x^{4}$ | |
Frobenius angles: | $\pm0.173686936480$, $\pm0.173686936480$ |
Angle rank: | $1$ (numerical) |
Jacobians: | $40$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $25281$ | $1062434025$ | $35165659044096$ | $1152017443113770025$ | $37738910498109592648041$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $136$ | $32428$ | $5930386$ | $1073358388$ | $194265859456$ | $35161851838678$ | $6364291175734096$ | $1151936659284147748$ | $208500535054664128906$ | $37738596846429369169948$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 40 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=x^6+14x^3+29$
- $y^2=65x^6+76x^5+110x^4+90x^3+127x^2+118x+73$
- $y^2=93x^6+126x^5+129x^4+95x^3+93x^2+50x+74$
- $y^2=125x^6+28x^5+109x^4+111x^3+116x^2+23x+180$
- $y^2=32x^6+23x^5+146x^4+127x^3+132x^2+53x+5$
- $y^2=24x^6+76x^5+30x^4+134x^3+123x^2+54x+28$
- $y^2=77x^6+86x^5+19x^4+113x^3+24x^2+104x+8$
- $y^2=176x^6+131x^5+12x^4+126x^3+94x^2+19x+36$
- $y^2=168x^6+127x^5+116x^4+52x^3+75x^2+146x+158$
- $y^2=40x^6+127x^5+63x^4+155x^3+134x^2+122x+89$
- $y^2=146x^6+59x^5+18x^4+145x^3+148x^2+113x+69$
- $y^2=171x^6+73x^5+133x^4+32x^3+7x^2+61x+159$
- $y^2=30x^6+31x^5+125x^4+145x^3+129x^2+120x+107$
- $y^2=100x^6+160x^5+177x^4+71x^3+126x^2+23x+11$
- $y^2=31x^6+164x^5+151x^4+62x^3+125x^2+81x+90$
- $y^2=85x^6+14x^5+7x^4+85x^3+174x^2+14x+96$
- $y^2=x^6+x^3+132$
- $y^2=131x^6+25x^5+140x^4+79x^3+27x^2+58x+133$
- $y^2=68x^6+9x^5+69x^4+121x^3+2x^2+129x+30$
- $y^2=173x^6+131x^5+66x^4+99x^3+77x^2+123x+175$
- and 20 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The isogeny class factors as 1.181.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-195}) \)$)$ |
Base change
This is a primitive isogeny class.