Invariants
| Level: | $330$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot10^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10D1 |
Level structure
| $\GL_2(\Z/330\Z)$-generators: | $\begin{bmatrix}5&206\\321&25\end{bmatrix}$, $\begin{bmatrix}63&124\\311&325\end{bmatrix}$, $\begin{bmatrix}71&319\\283&190\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 110.24.1.c.2 for the level structure with $-I$) |
| Cyclic 330-isogeny field degree: | $144$ |
| Cyclic 330-torsion field degree: | $11520$ |
| Full 330-torsion field degree: | $38016000$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 30.24.0-5.a.2.2 | $30$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 165.24.0-5.a.2.2 | $165$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 330.144.1-110.c.2.1 | $330$ | $3$ | $3$ | $1$ | $?$ | dimension zero |
| 330.240.5-110.e.1.2 | $330$ | $5$ | $5$ | $5$ | $?$ | not computed |
| 330.144.5-330.bi.1.5 | $330$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 330.192.5-330.i.1.4 | $330$ | $4$ | $4$ | $5$ | $?$ | not computed |