Invariants
| Level: | $238$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
| Genus: | $2 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $3$ are rational) | Cusp widths | $2^{3}\cdot14^{3}$ | Cusp orbits | $1^{3}\cdot3$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $3$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14D2 |
Level structure
| $\GL_2(\Z/238\Z)$-generators: | $\begin{bmatrix}15&186\\189&81\end{bmatrix}$, $\begin{bmatrix}236&237\\45&44\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 238.48.2.b.2 for the level structure with $-I$) |
| Cyclic 238-isogeny field degree: | $54$ |
| Cyclic 238-torsion field degree: | $5184$ |
| Full 238-torsion field degree: | $9870336$ |
Rational points
This modular curve has 3 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 7.48.0-7.a.2.2 | $7$ | $2$ | $2$ | $0$ | $0$ |
| 238.48.0-7.a.2.1 | $238$ | $2$ | $2$ | $0$ | $?$ |
| 238.32.0-238.b.1.3 | $238$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 238.288.4-238.b.2.4 | $238$ | $3$ | $3$ | $4$ |