Invariants
| Level: | $150$ | $\SL_2$-level: | $150$ | Newform level: | $1$ | ||
| Index: | $360$ | $\PSL_2$-index: | $360$ | ||||
| Genus: | $21 = 1 + \frac{ 360 }{12} - \frac{ 16 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{10}\cdot150^{2}$ | Cusp orbits | $1^{2}\cdot2\cdot4^{2}$ | ||
| Elliptic points: | $16$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 21$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 21$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 150A21 |
Level structure
| $\GL_2(\Z/150\Z)$-generators: | $\begin{bmatrix}84&137\\23&48\end{bmatrix}$, $\begin{bmatrix}85&37\\52&125\end{bmatrix}$, $\begin{bmatrix}146&57\\15&103\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 150-isogeny field degree: | $12$ |
| Cyclic 150-torsion field degree: | $480$ |
| Full 150-torsion field degree: | $240000$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 30.72.1.o.1 | $30$ | $5$ | $5$ | $1$ | $1$ |
| 75.180.8.a.1 | $75$ | $2$ | $2$ | $8$ | $?$ |
| 150.180.10.a.1 | $150$ | $2$ | $2$ | $10$ | $?$ |
| 150.180.11.b.1 | $150$ | $2$ | $2$ | $11$ | $?$ |