Invariants
| Level: | $330$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
| Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $2^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10A5 |
Level structure
| $\GL_2(\Z/330\Z)$-generators: | $\begin{bmatrix}26&139\\147&284\end{bmatrix}$, $\begin{bmatrix}85&106\\228&107\end{bmatrix}$, $\begin{bmatrix}296&105\\295&241\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 330-isogeny field degree: | $144$ |
| Cyclic 330-torsion field degree: | $11520$ |
| Full 330-torsion field degree: | $15206400$ |
Rational points
This modular curve has no $\Q_p$ points for $p=19$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.60.2.c.1 | $10$ | $2$ | $2$ | $2$ | $0$ |
| 165.60.0.a.1 | $165$ | $2$ | $2$ | $0$ | $?$ |
| 330.24.1.ba.1 | $330$ | $5$ | $5$ | $1$ | $?$ |
| 330.24.1.ba.2 | $330$ | $5$ | $5$ | $1$ | $?$ |
| 330.60.3.n.1 | $330$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 330.360.13.ba.1 | $330$ | $3$ | $3$ | $13$ |