Invariants
| Level: | $308$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $288$ | $\PSL_2$-index: | $144$ | ||||
| Genus: | $4 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 18 }{2}$ | ||||||
| Cusps: | $18$ (of which $3$ are rational) | Cusp widths | $2^{9}\cdot14^{9}$ | Cusp orbits | $1^{3}\cdot2^{3}\cdot3\cdot6$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $3$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 14B4 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}71&250\\252&185\end{bmatrix}$, $\begin{bmatrix}159&36\\262&245\end{bmatrix}$, $\begin{bmatrix}231&216\\120&149\end{bmatrix}$, $\begin{bmatrix}254&117\\195&150\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 308.144.4.d.2 for the level structure with $-I$) |
| Cyclic 308-isogeny field degree: | $24$ |
| Cyclic 308-torsion field degree: | $2880$ |
| Full 308-torsion field degree: | $8870400$ |
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 |
|---|---|---|---|---|---|
| 14.144.1-14.a.2.1 | $14$ | $2$ | $2$ | $1$ | $0$ |
| 308.96.2-308.b.2.5 | $308$ | $3$ | $3$ | $2$ | $?$ |
| 308.96.2-308.h.1.5 | $308$ | $3$ | $3$ | $2$ | $?$ |
| 308.144.1-14.a.2.4 | $308$ | $2$ | $2$ | $1$ | $?$ |