Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 49 x + 959 x^{2} - 8869 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0675982025699$, $\pm0.180470077574$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1135173.1 |
Galois group: | $D_{4}$ |
Jacobians: | $10$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $24803$ | $1057575117$ | $35142370370207$ | $1151935362697290453$ | $37738676653843304208848$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $133$ | $32279$ | $5926459$ | $1073281915$ | $194264655718$ | $35161836321215$ | $6364291021791115$ | $1151936658475079923$ | $208500535064710937965$ | $37738596846842066811974$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 10 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=7x^6+73x^5+21x^4+98x^3+142x^2+179x+20$
- $y^2=158x^6+154x^5+74x^4+129x^3+57x^2+11$
- $y^2=37x^6+155x^5+88x^3+73x^2+110x+112$
- $y^2=8x^6+93x^5+84x^4+119x^3+41x^2+55x+58$
- $y^2=13x^6+106x^5+132x^4+43x^3+22x^2+163x+97$
- $y^2=124x^6+142x^5+170x^4+76x^3+41x^2+146x+156$
- $y^2=87x^6+30x^5+154x^4+109x^3+154x^2+91x+151$
- $y^2=162x^6+121x^5+145x^4+77x^3+109x^2+x+107$
- $y^2=172x^6+169x^5+4x^4+59x^3+120x^2+55x+107$
- $y^2=150x^6+48x^5+150x^4+157x^3+159x^2+133x+17$
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 4.0.1135173.1. |
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.bx_bkx | $2$ | (not in LMFDB) |