Invariants
| Level: | $152$ | $\SL_2$-level: | $152$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $18 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $2^{2}\cdot8\cdot38^{2}\cdot152$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $7 \le \gamma \le 18$ | ||||||
| $\overline{\Q}$-gonality: | $7 \le \gamma \le 18$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 152A18 |
Level structure
| $\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}21&74\\90&113\end{bmatrix}$, $\begin{bmatrix}52&135\\109&26\end{bmatrix}$, $\begin{bmatrix}64&147\\75&144\end{bmatrix}$, $\begin{bmatrix}99&8\\26&41\end{bmatrix}$, $\begin{bmatrix}101&72\\96&49\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 152.240.18.f.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 6 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 |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.6 | $8$ | $40$ | $40$ | $0$ | $0$ |
| 19.40.1-19.a.1.1 | $19$ | $12$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 76.240.8-76.c.1.4 | $76$ | $2$ | $2$ | $8$ | $?$ |
| 152.240.8-76.c.1.23 | $152$ | $2$ | $2$ | $8$ | $?$ |