Invariants
Level: | $80$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{8}\cdot16^{2}$ | Cusp orbits | $2^{5}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G0 |
Level structure
$\GL_2(\Z/80\Z)$-generators: | $\begin{bmatrix}3&32\\35&21\end{bmatrix}$, $\begin{bmatrix}11&16\\34&15\end{bmatrix}$, $\begin{bmatrix}13&0\\75&67\end{bmatrix}$, $\begin{bmatrix}55&8\\32&27\end{bmatrix}$, $\begin{bmatrix}71&24\\58&43\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 16.48.0.k.1 for the level structure with $-I$) |
Cyclic 80-isogeny field degree: | $12$ |
Cyclic 80-torsion field degree: | $384$ |
Full 80-torsion field degree: | $122880$ |
Models
Smooth plane model Smooth plane model
$ 0 $ | $=$ | $ x^{2} + 2 y^{2} + 4 z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
40.48.0-8.q.1.4 | $40$ | $2$ | $2$ | $0$ | $0$ |
80.48.0-16.f.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-16.f.1.16 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-16.f.2.8 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-16.f.2.10 | $80$ | $2$ | $2$ | $0$ | $?$ |
80.48.0-8.q.1.3 | $80$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.