Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot16^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16I3 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}89&144\\40&29\end{bmatrix}$, $\begin{bmatrix}141&224\\116&55\end{bmatrix}$, $\begin{bmatrix}209&32\\146&201\end{bmatrix}$, $\begin{bmatrix}209&296\\86&15\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.96.3.cv.2 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $40$ |
| Cyclic 304-torsion field degree: | $2880$ |
| Full 304-torsion field degree: | $15759360$ |
Rational points
This modular curve has 2 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 |
|---|---|---|---|---|---|
| 16.96.0-16.d.1.2 | $16$ | $2$ | $2$ | $0$ | $0$ |
| 152.96.1-152.bv.1.1 | $152$ | $2$ | $2$ | $1$ | $?$ |
| 304.96.0-16.d.1.5 | $304$ | $2$ | $2$ | $0$ | $?$ |
| 304.96.1-152.bv.1.4 | $304$ | $2$ | $2$ | $1$ | $?$ |
| 304.96.2-304.d.2.7 | $304$ | $2$ | $2$ | $2$ | $?$ |
| 304.96.2-304.d.2.11 | $304$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 304.384.5-304.ea.1.3 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.ec.1.4 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.ee.2.4 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.eg.2.16 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.el.2.4 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.em.2.2 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.en.1.2 | $304$ | $2$ | $2$ | $5$ |
| 304.384.5-304.eo.1.2 | $304$ | $2$ | $2$ | $5$ |