Invariants
| Level: | $330$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
| Index: | $40$ | $\PSL_2$-index: | $40$ | ||||
| Genus: | $1 = 1 + \frac{ 40 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (none of which are rational) | Cusp widths | $10^{4}$ | Cusp orbits | $4$ | ||
| Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 40$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 10H1 |
Level structure
| $\GL_2(\Z/330\Z)$-generators: | $\begin{bmatrix}220&189\\31&104\end{bmatrix}$, $\begin{bmatrix}263&271\\189&44\end{bmatrix}$, $\begin{bmatrix}307&53\\25&108\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 330-isogeny field degree: | $864$ |
| Cyclic 330-torsion field degree: | $69120$ |
| Full 330-torsion field degree: | $45619200$ |
Jacobian
| Conductor: | $?$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | not computed |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 6.2.0.a.1 | $6$ | $20$ | $20$ | $0$ | $0$ | full Jacobian |
| 55.20.0.b.1 | $55$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 30.20.1.a.1 | $30$ | $2$ | $2$ | $1$ | $1$ | dimension zero |
| 55.20.0.b.1 | $55$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 330.20.0.a.1 | $330$ | $2$ | $2$ | $0$ | $?$ | 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 |
|---|---|---|---|---|---|---|
| 330.120.5.f.1 | $330$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 330.120.5.h.1 | $330$ | $3$ | $3$ | $5$ | $?$ | not computed |
| 330.120.7.b.1 | $330$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 330.120.9.u.1 | $330$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 330.160.9.f.1 | $330$ | $4$ | $4$ | $9$ | $?$ | not computed |