Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 47 x + 911 x^{2} - 8507 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.110478730961$, $\pm0.201428511501$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.398333.1 |
Galois group: | $D_{4}$ |
Jacobians: | $21$ |
This isogeny class is simple and geometrically 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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $25119$ | $1060700013$ | $35156541071331$ | $1151981523639451413$ | $37738796109746922216144$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $135$ | $32375$ | $5928849$ | $1073324923$ | $194265270630$ | $35161843537343$ | $6364291092502401$ | $1151936659092513139$ | $208500535070898045471$ | $37738596846935232325190$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=54x^6+76x^5+60x^4+99x^3+71x^2+173x+76$
- $y^2=83x^6+43x^5+112x^4+4x^3+24x^2+110x+58$
- $y^2=110x^6+126x^5+86x^4+116x^3+116x^2+127x+128$
- $y^2=108x^6+22x^5+5x^4+73x^3+32x^2+74x+90$
- $y^2=90x^6+68x^5+132x^4+94x^3+43x^2+148x+164$
- $y^2=31x^6+149x^5+16x^4+108x^3+167x^2+40x+114$
- $y^2=110x^6+173x^5+13x^4+72x^3+90x^2+68x+112$
- $y^2=45x^6+170x^5+98x^4+57x^3+61x^2+84x+43$
- $y^2=70x^6+113x^5+99x^4+10x^3+44x^2+149x+132$
- $y^2=97x^5+46x^4+164x^3+120x^2+97x+82$
- $y^2=159x^6+103x^5+88x^4+55x^3+35x^2+27x+22$
- $y^2=17x^6+24x^5+170x^4+167x^3+77x^2+103x+66$
- $y^2=130x^6+107x^5+75x^4+48x^3+50x^2+162x+81$
- $y^2=46x^6+97x^5+136x^4+17x^3+175x^2+46x+2$
- $y^2=57x^6+87x^5+32x^4+101x^3+180x^2+150x+80$
- $y^2=45x^6+144x^5+22x^4+21x^3+40x^2+14x+22$
- $y^2=112x^6+116x^5+179x^4+103x^3+33x^2+85x+21$
- $y^2=19x^6+53x^5+2x^4+175x^3+103x^2+x+152$
- $y^2=38x^6+152x^5+103x^4+117x^3+18x^2+40x+162$
- $y^2=89x^6+157x^5+5x^4+124x^3+127x^2+143x+37$
- $y^2=154x^6+46x^5+123x^4+74x^3+153x^2+169x+125$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The endomorphism algebra of this simple isogeny class is 4.0.398333.1. |
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 |
---|---|---|
2.181.bv_bjb | $2$ | (not in LMFDB) |