Invariants
| Level: | $114$ | $\SL_2$-level: | $114$ | Newform level: | $1$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (all of which are rational) | Cusp widths | $1\cdot2\cdot3\cdot6\cdot19\cdot38\cdot57\cdot114$ | Cusp orbits | $1^{8}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 17$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 17$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 114A17 |
Level structure
| $\GL_2(\Z/114\Z)$-generators: | $\begin{bmatrix}25&5\\0&59\end{bmatrix}$, $\begin{bmatrix}41&98\\0&49\end{bmatrix}$, $\begin{bmatrix}49&10\\0&91\end{bmatrix}$, $\begin{bmatrix}91&92\\0&55\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 114.240.17.a.1 for the level structure with $-I$) |
| Cyclic 114-isogeny field degree: | $1$ |
| Cyclic 114-torsion field degree: | $36$ |
| Full 114-torsion field degree: | $73872$ |
Rational points
This modular curve has 8 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 |
|---|---|---|---|---|---|
| 6.24.0-6.a.1.3 | $6$ | $20$ | $20$ | $0$ | $0$ |
| $X_0(19)$ | $19$ | $24$ | $12$ | $1$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 6.24.0-6.a.1.3 | $6$ | $20$ | $20$ | $0$ | $0$ |
| 114.160.5-57.a.1.8 | $114$ | $3$ | $3$ | $5$ | $?$ |