Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{8}\cdot8^{12}\cdot16^{4}$ | Cusp orbits | $2^{4}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16O5 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}163&244\\240&17\end{bmatrix}$, $\begin{bmatrix}177&28\\36&281\end{bmatrix}$, $\begin{bmatrix}195&264\\216&121\end{bmatrix}$, $\begin{bmatrix}197&264\\8&177\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.192.5.a.2 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $80$ |
| Cyclic 304-torsion field degree: | $2880$ |
| Full 304-torsion field degree: | $7879680$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 16.192.2-16.a.1.2 | $16$ | $2$ | $2$ | $2$ | $0$ |
| 152.192.1-152.x.2.5 | $152$ | $2$ | $2$ | $1$ | $?$ |
| 304.192.1-152.x.2.3 | $304$ | $2$ | $2$ | $1$ | $?$ |
| 304.192.2-16.a.1.6 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.192.2-304.a.1.1 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.192.2-304.a.1.26 | $304$ | $2$ | $2$ | $2$ | $?$ |