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: | $\begin{bmatrix}33&76\\68&69\end{bmatrix}$, $\begin{bmatrix}77&76\\93&103\end{bmatrix}$, $\begin{bmatrix}101&0\\148&83\end{bmatrix}$, $\begin{bmatrix}119&76\\22&47\end{bmatrix}$, $\begin{bmatrix}127&0\\11&23\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 76.240.17.k.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
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
152.24.0-76.g.1.5 | $152$ | $20$ | $20$ | $0$ | $?$ |
152.240.8-76.c.1.3 | $152$ | $2$ | $2$ | $8$ | $?$ |
152.240.8-76.c.1.23 | $152$ | $2$ | $2$ | $8$ | $?$ |