Invariants
| Level: | $210$ | $\SL_2$-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
| $\GL_2(\Z/210\Z)$-generators: | $\begin{bmatrix}31&195\\25&86\end{bmatrix}$, $\begin{bmatrix}59&38\\54&55\end{bmatrix}$, $\begin{bmatrix}145&134\\57&23\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 210.120.5.r.1 for the level structure with $-I$) |
| Cyclic 210-isogeny field degree: | $96$ |
| Cyclic 210-torsion field degree: | $1152$ |
| Full 210-torsion field degree: | $1161216$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{arith}}(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ |
| 42.2.0.a.1 | $42$ | $120$ | $60$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_{\mathrm{arith}}(5)$ | $5$ | $2$ | $2$ | $0$ | $0$ |
| 210.120.0-5.a.1.2 | $210$ | $2$ | $2$ | $0$ | $?$ |
| 210.48.1-210.s.1.5 | $210$ | $5$ | $5$ | $1$ | $?$ |
| 210.48.1-210.s.2.5 | $210$ | $5$ | $5$ | $1$ | $?$ |