Invariants
| Level: | $308$ | $\SL_2$-level: | $4$ | ||||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $0 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (none of which are rational) | Cusp widths | $4^{6}$ | Cusp orbits | $2^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $1$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 4G0 |
Level structure
| $\GL_2(\Z/308\Z)$-generators: | $\begin{bmatrix}103&146\\156&91\end{bmatrix}$, $\begin{bmatrix}141&286\\214&19\end{bmatrix}$, $\begin{bmatrix}259&274\\162&165\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 44.24.0.b.1 for the level structure with $-I$) |
| Cyclic 308-isogeny field degree: | $192$ |
| Cyclic 308-torsion field degree: | $23040$ |
| Full 308-torsion field degree: | $53222400$ |
Models
Smooth plane model Smooth plane model
| $ 0 $ | $=$ | $ 25 x^{2} + 5 x y + 3 y^{2} + 44 z^{2} $ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 28.24.0-4.a.1.2 | $28$ | $2$ | $2$ | $0$ | $0$ |
| 308.24.0-4.a.1.1 | $308$ | $2$ | $2$ | $0$ | $?$ |
| 308.24.0-44.b.1.1 | $308$ | $2$ | $2$ | $0$ | $?$ |
| 308.24.0-44.b.1.2 | $308$ | $2$ | $2$ | $0$ | $?$ |
| 308.24.0-44.b.1.4 | $308$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 308.384.11-308.b.1.6 | $308$ | $8$ | $8$ | $11$ |