Invariants
| Level: | $296$ | $\SL_2$-level: | $148$ | Newform level: | $1$ | ||
| Index: | $456$ | $\PSL_2$-index: | $228$ | ||||
| Genus: | $17 = 1 + \frac{ 228 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (all of which are rational) | Cusp widths | $1^{2}\cdot4\cdot37^{2}\cdot148$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $5 \le \gamma \le 17$ | ||||||
| $\overline{\Q}$-gonality: | $5 \le \gamma \le 17$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 148A17 |
Level structure
| $\GL_2(\Z/296\Z)$-generators: | $\begin{bmatrix}29&290\\102&69\end{bmatrix}$, $\begin{bmatrix}41&136\\204&121\end{bmatrix}$, $\begin{bmatrix}68&251\\29&142\end{bmatrix}$, $\begin{bmatrix}147&264\\158&253\end{bmatrix}$, $\begin{bmatrix}236&155\\69&26\end{bmatrix}$, $\begin{bmatrix}259&190\\250&199\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 148.228.17.c.1 for the level structure with $-I$) |
| Cyclic 296-isogeny field degree: | $2$ |
| Cyclic 296-torsion field degree: | $288$ |
| Full 296-torsion field degree: | $6137856$ |
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.1.3 | $8$ | $38$ | $38$ | $0$ | $0$ |
| $X_0(37)$ | $37$ | $12$ | $6$ | $2$ | $1$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 8.12.0-4.c.1.3 | $8$ | $38$ | $38$ | $0$ | $0$ |