Invariants
| Level: | $150$ | $\SL_2$-level: | $50$ | Newform level: | $1$ | ||
| Index: | $150$ | $\PSL_2$-index: | $150$ | ||||
| Genus: | $9 = 1 + \frac{ 150 }{12} - \frac{ 4 }{4} - \frac{ 0 }{3} - \frac{ 7 }{2}$ | ||||||
| Cusps: | $7$ (none of which are rational) | Cusp widths | $10^{5}\cdot50^{2}$ | Cusp orbits | $2\cdot5$ | ||
| Elliptic points: | $4$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 50E9 |
Level structure
| $\GL_2(\Z/150\Z)$-generators: | $\begin{bmatrix}53&119\\107&130\end{bmatrix}$, $\begin{bmatrix}57&92\\50&73\end{bmatrix}$, $\begin{bmatrix}100&113\\51&100\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 150-isogeny field degree: | $120$ |
| Cyclic 150-torsion field degree: | $4800$ |
| Full 150-torsion field degree: | $576000$ |
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 |
|---|---|---|---|---|---|
| 25.75.2.a.1 | $25$ | $2$ | $2$ | $2$ | $2$ |
| 30.30.1.c.1 | $30$ | $5$ | $5$ | $1$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 150.300.19.a.1 | $150$ | $2$ | $2$ | $19$ |
| 150.300.19.g.1 | $150$ | $2$ | $2$ | $19$ |
| 150.300.19.t.1 | $150$ | $2$ | $2$ | $19$ |
| 150.300.19.v.1 | $150$ | $2$ | $2$ | $19$ |
| 300.300.19.b.1 | $300$ | $2$ | $2$ | $19$ |
| 300.300.19.p.1 | $300$ | $2$ | $2$ | $19$ |
| 300.300.19.bm.1 | $300$ | $2$ | $2$ | $19$ |
| 300.300.19.bs.1 | $300$ | $2$ | $2$ | $19$ |