Invariants
| Level: | $308$ | $\SL_2$-level: | $44$ | Newform level: | $1$ | ||
| Index: | $144$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $9 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot22^{2}\cdot44^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 9$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 9$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 44B9 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}9&286\\210&307\end{bmatrix}$, $\begin{bmatrix}71&110\\84&181\end{bmatrix}$, $\begin{bmatrix}131&88\\210&213\end{bmatrix}$, $\begin{bmatrix}151&88\\52&207\end{bmatrix}$, $\begin{bmatrix}251&264\\76&39\end{bmatrix}$, $\begin{bmatrix}289&0\\284&107\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 308.288.9-308.b.1.1, 308.288.9-308.b.1.2, 308.288.9-308.b.1.3, 308.288.9-308.b.1.4, 308.288.9-308.b.1.5, 308.288.9-308.b.1.6, 308.288.9-308.b.1.7, 308.288.9-308.b.1.8, 308.288.9-308.b.1.9, 308.288.9-308.b.1.10, 308.288.9-308.b.1.11, 308.288.9-308.b.1.12, 308.288.9-308.b.1.13, 308.288.9-308.b.1.14, 308.288.9-308.b.1.15, 308.288.9-308.b.1.16, 308.288.9-308.b.1.17, 308.288.9-308.b.1.18, 308.288.9-308.b.1.19, 308.288.9-308.b.1.20 |
| Cyclic 308-isogeny field degree: | $16$ |
| Cyclic 308-torsion field degree: | $1920$ |
| Full 308-torsion field degree: | $17740800$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| $X_0(11)$ | $11$ | $12$ | $12$ | $1$ | $0$ |
| 28.12.0.b.1 | $28$ | $12$ | $12$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 22.72.4.a.1 | $22$ | $2$ | $2$ | $4$ | $0$ |
| 28.12.0.b.1 | $28$ | $12$ | $12$ | $0$ | $0$ |
| 308.72.4.c.1 | $308$ | $2$ | $2$ | $4$ | $?$ |
| 308.72.5.c.1 | $308$ | $2$ | $2$ | $5$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 308.288.17.d.1 | $308$ | $2$ | $2$ | $17$ |
| 308.288.17.d.2 | $308$ | $2$ | $2$ | $17$ |
| 308.288.17.d.3 | $308$ | $2$ | $2$ | $17$ |
| 308.288.17.d.4 | $308$ | $2$ | $2$ | $17$ |
| 308.288.19.b.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.c.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.i.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.j.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.l.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.l.2 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.p.1 | $308$ | $2$ | $2$ | $19$ |
| 308.288.19.p.2 | $308$ | $2$ | $2$ | $19$ |