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: | $8$ (all of which are rational) | Cusp widths | $1^{2}\cdot2\cdot8\cdot19^{2}\cdot38\cdot152$ | Cusp orbits | $1^{8}$ | ||
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: | $8$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 152A17 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}23&87\\0&143\end{bmatrix}$, $\begin{bmatrix}37&26\\0&119\end{bmatrix}$, $\begin{bmatrix}55&78\\0&49\end{bmatrix}$, $\begin{bmatrix}73&148\\0&139\end{bmatrix}$, $\begin{bmatrix}93&99\\0&121\end{bmatrix}$, $\begin{bmatrix}123&81\\0&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.240.17.bl.1 for the level structure with $-I$) |
Cyclic 152-isogeny field degree: | $1$ |
Cyclic 152-torsion field degree: | $72$ |
Full 152-torsion field degree: | $393984$ |
Rational points
This modular curve has 8 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.n.1.8 | $8$ | $20$ | $20$ | $0$ | $0$ |
$X_0(19)$ | $19$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.24.0-8.n.1.8 | $8$ | $20$ | $20$ | $0$ | $0$ |
152.240.8-76.c.1.17 | $152$ | $2$ | $2$ | $8$ | $?$ |
152.240.8-76.c.1.23 | $152$ | $2$ | $2$ | $8$ | $?$ |