Invariants
| Level: | $304$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $8^{2}\cdot16^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3$ | ||||||
| $\overline{\Q}$-gonality: | $3$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 16A3 |
Level structure
| $\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}166&173\\269&78\end{bmatrix}$, $\begin{bmatrix}189&182\\158&189\end{bmatrix}$, $\begin{bmatrix}221&292\\196&49\end{bmatrix}$, $\begin{bmatrix}237&228\\108&169\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 304.48.3.bd.1 for the level structure with $-I$) |
| Cyclic 304-isogeny field degree: | $80$ |
| Cyclic 304-torsion field degree: | $11520$ |
| Full 304-torsion field degree: | $31518720$ |
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 |
|---|---|---|---|---|---|
| 8.48.1-8.n.1.4 | $8$ | $2$ | $2$ | $1$ | $0$ |
| 304.48.1-8.n.1.1 | $304$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 304.192.5-304.ea.1.1 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.eb.2.5 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.fv.1.2 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.fx.2.4 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.gh.2.4 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.gj.2.3 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.gt.2.3 | $304$ | $2$ | $2$ | $5$ |
| 304.192.5-304.gu.2.1 | $304$ | $2$ | $2$ | $5$ |