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 | $2^{2}\cdot4^{2}\cdot38^{2}\cdot76^{2}$ | 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: | 76A17 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}23&76\\73&23\end{bmatrix}$, $\begin{bmatrix}23&76\\86&87\end{bmatrix}$, $\begin{bmatrix}71&76\\127&79\end{bmatrix}$, $\begin{bmatrix}79&0\\76&17\end{bmatrix}$, $\begin{bmatrix}145&76\\78&31\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.240.17.w.1 for the level structure with $-I$) |
| Cyclic 152-isogeny field degree: | $2$ |
| Cyclic 152-torsion field degree: | $72$ |
| 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.k.1.3 | $8$ | $20$ | $20$ | $0$ | $0$ |
| $X_0(19)$ | $19$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.24.0-8.k.1.3 | $8$ | $20$ | $20$ | $0$ | $0$ |
| 152.240.8-76.c.1.23 | $152$ | $2$ | $2$ | $8$ | $?$ |
| 152.240.8-76.c.1.26 | $152$ | $2$ | $2$ | $8$ | $?$ |