Invariants
| Level: | $330$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $60$ | $\PSL_2$-index: | $60$ | ||||
| Genus: | $3 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $10^{6}$ | Cusp orbits | $2\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10B3 |
Level structure
| $\GL_2(\Z/330\Z)$-generators: | $\begin{bmatrix}89&194\\106&29\end{bmatrix}$, $\begin{bmatrix}179&319\\159&206\end{bmatrix}$, $\begin{bmatrix}218&65\\105&178\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 330-isogeny field degree: | $288$ |
| Cyclic 330-torsion field degree: | $23040$ |
| Full 330-torsion field degree: | $30412800$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.30.1.b.1 | $30$ | $2$ | $2$ | $1$ | $1$ |
| 110.30.2.d.1 | $110$ | $2$ | $2$ | $2$ | $?$ |
| 165.30.0.a.1 | $165$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 330.180.7.bb.1 | $330$ | $3$ | $3$ | $7$ |
| 330.180.13.gu.1 | $330$ | $3$ | $3$ | $13$ |
| 330.240.15.bo.1 | $330$ | $4$ | $4$ | $15$ |