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: | $24$ (of which $4$ are rational) | Cusp widths | $2^{8}\cdot4^{4}\cdot8^{4}\cdot16^{8}$ | Cusp orbits | $1^{4}\cdot4^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 5$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16N5 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}23&16\\137&17\end{bmatrix}$, $\begin{bmatrix}87&48\\191&73\end{bmatrix}$, $\begin{bmatrix}191&160\\265&185\end{bmatrix}$, $\begin{bmatrix}301&112\\260&217\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.192.5.gu.3 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $20$ |
| Cyclic 304-torsion field degree: | $720$ |
| Full 304-torsion field degree: | $7879680$ |
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 |
|---|---|---|---|---|---|
| 16.192.1-16.m.2.3 | $16$ | $2$ | $2$ | $1$ | $0$ |
| 304.192.1-16.m.2.2 | $304$ | $2$ | $2$ | $1$ | $?$ |
| 304.192.2-304.i.1.1 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.192.2-304.i.1.15 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.192.2-304.l.1.1 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.192.2-304.l.1.14 | $304$ | $2$ | $2$ | $2$ | $?$ |