Invariants
| Level: | $248$ | $\SL_2$-level: | $248$ | Newform level: | $1$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $14 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $1^{2}\cdot4\cdot31^{2}\cdot124$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 14$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 124A14 |
Level structure
| $\GL_2(\Z/248\Z)$-generators: | $\begin{bmatrix}46&65\\117&118\end{bmatrix}$, $\begin{bmatrix}94&83\\227&74\end{bmatrix}$, $\begin{bmatrix}95&190\\16&21\end{bmatrix}$, $\begin{bmatrix}160&5\\81&208\end{bmatrix}$, $\begin{bmatrix}174&19\\3&66\end{bmatrix}$, $\begin{bmatrix}196&79\\123&152\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 124.192.14.c.1 for the level structure with $-I$) |
| Cyclic 248-isogeny field degree: | $2$ |
| Cyclic 248-torsion field degree: | $240$ |
| Full 248-torsion field degree: | $3571200$ |
Rational points
This modular curve has 6 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 |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.6 | $8$ | $32$ | $32$ | $0$ | $0$ |
| $X_0(31)$ | $31$ | $12$ | $6$ | $2$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.6 | $8$ | $32$ | $32$ | $0$ | $0$ |