Invariants
| Level: | $220$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $240$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $1^{2}\cdot2\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10A5 |
Level structure
| $\GL_2(\Z/220\Z)$-generators: | $\begin{bmatrix}39&33\\194&135\end{bmatrix}$, $\begin{bmatrix}195&64\\217&143\end{bmatrix}$, $\begin{bmatrix}209&188\\34&25\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 220.120.5.x.1 for the level structure with $-I$) |
| Cyclic 220-isogeny field degree: | $72$ |
| Cyclic 220-torsion field degree: | $1440$ |
| Full 220-torsion field degree: | $2534400$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{arith}}(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ |
| 220.120.0-5.a.1.3 | $220$ | $2$ | $2$ | $0$ | $?$ |
| 220.48.1-220.j.1.8 | $220$ | $5$ | $5$ | $1$ | $?$ |
| 220.48.1-220.j.2.4 | $220$ | $5$ | $5$ | $1$ | $?$ |