Invariants
| Level: | $152$ | $\SL_2$-level: | $152$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot19^{2}\cdot38\cdot152$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $6 \le \gamma \le 17$ | ||||||
| $\overline{\Q}$-gonality: | $6 \le \gamma \le 17$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 152A17 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}28&87\\41&74\end{bmatrix}$, $\begin{bmatrix}41&116\\146&87\end{bmatrix}$, $\begin{bmatrix}44&49\\85&84\end{bmatrix}$, $\begin{bmatrix}84&63\\25&122\end{bmatrix}$, $\begin{bmatrix}128&65\\13&104\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.240.17.bq.1 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $2$ |
| Cyclic 152-torsion field degree: | $144$ |
| Full 152-torsion field degree: | $393984$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal 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 |
|---|---|---|---|---|---|
| 8.24.0-8.o.1.2 | $8$ | $20$ | $20$ | $0$ | $0$ |
| $X_0(19)$ | $19$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.o.1.2 | $8$ | $20$ | $20$ | $0$ | $0$ |
| 152.240.8-76.c.1.11 | $152$ | $2$ | $2$ | $8$ | $?$ |
| 152.240.8-76.c.1.23 | $152$ | $2$ | $2$ | $8$ | $?$ |