Invariants
| Level: | $308$ | $\SL_2$-level: | $28$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $11 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $4^{6}\cdot28^{6}$ | Cusp orbits | $2^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 11$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 28E11 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}95&72\\252&171\end{bmatrix}$, $\begin{bmatrix}111&140\\96&205\end{bmatrix}$, $\begin{bmatrix}257&82\\18&217\end{bmatrix}$, $\begin{bmatrix}305&126\\2&225\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 308.192.11.b.1 for the level structure with $-I$) |
| Cyclic 308-isogeny field degree: | $24$ |
| Cyclic 308-torsion field degree: | $2880$ |
| Full 308-torsion field degree: | $6652800$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 28.192.5-28.a.1.9 | $28$ | $2$ | $2$ | $5$ | $1$ |
| 308.48.0-44.b.1.2 | $308$ | $8$ | $8$ | $0$ | $?$ |
| 308.192.5-28.a.1.5 | $308$ | $2$ | $2$ | $5$ | $?$ |
| 308.192.5-308.b.1.2 | $308$ | $2$ | $2$ | $5$ | $?$ |
| 308.192.5-308.b.1.8 | $308$ | $2$ | $2$ | $5$ | $?$ |
| 308.192.5-308.b.1.13 | $308$ | $2$ | $2$ | $5$ | $?$ |