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: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-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: | $\begin{bmatrix}67&286\\164&299\end{bmatrix}$, $\begin{bmatrix}235&144\\22&21\end{bmatrix}$, $\begin{bmatrix}287&118\\218&41\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 308.24.0.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
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known 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 | $28$ | $2$ | $2$ | $0$ | $0$ |
44.24.0-4.a.1.1 | $44$ | $2$ | $2$ | $0$ | $0$ |
308.24.0-308.b.1.3 | $308$ | $2$ | $2$ | $0$ | $?$ |
308.24.0-308.b.1.4 | $308$ | $2$ | $2$ | $0$ | $?$ |
308.24.0-308.b.1.7 | $308$ | $2$ | $2$ | $0$ | $?$ |
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.e.1.2 | $308$ | $8$ | $8$ | $11$ |