Invariants
| Level: | $308$ | $\SL_2$-level: | $14$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-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
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}1&224\\49&211\end{bmatrix}$, $\begin{bmatrix}63&296\\258&221\end{bmatrix}$, $\begin{bmatrix}166&293\\185&37\end{bmatrix}$, $\begin{bmatrix}172&57\\137&231\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 308.96.2-308.b.2.1, 308.96.2-308.b.2.2, 308.96.2-308.b.2.3, 308.96.2-308.b.2.4, 308.96.2-308.b.2.5, 308.96.2-308.b.2.6, 308.96.2-308.b.2.7, 308.96.2-308.b.2.8 |
| Cyclic 308-isogeny field degree: | $72$ |
| Cyclic 308-torsion field degree: | $8640$ |
| Full 308-torsion field degree: | $53222400$ |
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 |
|---|---|---|---|---|---|
| 7.24.0.a.2 | $7$ | $2$ | $2$ | $0$ | $0$ |
| 308.16.0.b.1 | $308$ | $3$ | $3$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 308.144.4.d.2 | $308$ | $3$ | $3$ | $4$ |
| 308.192.11.br.2 | $308$ | $4$ | $4$ | $11$ |
| 308.336.17.br.1 | $308$ | $7$ | $7$ | $17$ |