Invariants
| Level: | $308$ | $\SL_2$-level: | $4$ | ||||
| Index: | $24$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4G0 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}9&276\\194&183\end{bmatrix}$, $\begin{bmatrix}65&186\\234&187\end{bmatrix}$, $\begin{bmatrix}77&38\\218&271\end{bmatrix}$, $\begin{bmatrix}291&78\\266&5\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 308.48.0-308.b.1.1, 308.48.0-308.b.1.2, 308.48.0-308.b.1.3, 308.48.0-308.b.1.4 |
| Cyclic 308-isogeny field degree: | $192$ |
| Cyclic 308-torsion field degree: | $23040$ |
| Full 308-torsion field degree: | $106444800$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
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 |
|---|---|---|---|---|---|
| 4.12.0.a.1 | $4$ | $2$ | $2$ | $0$ | $0$ |
| 308.12.0.b.1 | $308$ | $2$ | $2$ | $0$ | $?$ |
| 308.12.0.bl.1 | $308$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 308.192.11.e.1 | $308$ | $8$ | $8$ | $11$ |
| 308.288.19.e.1 | $308$ | $12$ | $12$ | $19$ |