Invariants
| Level: | $312$ | $\SL_2$-level: | $24$ | 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: | $6$ (all of which are rational) | Cusp widths | $2^{2}\cdot6^{2}\cdot8\cdot24$ | Cusp orbits | $1^{6}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $6$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 24F2 |
Level structure
| $\GL_2(\Z/312\Z)$-generators: | $\begin{bmatrix}6&115\\181&228\end{bmatrix}$, $\begin{bmatrix}31&20\\60&107\end{bmatrix}$, $\begin{bmatrix}163&290\\94&291\end{bmatrix}$, $\begin{bmatrix}257&184\\308&69\end{bmatrix}$, $\begin{bmatrix}279&232\\242&13\end{bmatrix}$, $\begin{bmatrix}303&310\\4&261\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 312.48.2.h.1 for the level structure with $-I$) |
| Cyclic 312-isogeny field degree: | $28$ |
| Cyclic 312-torsion field degree: | $2688$ |
| Full 312-torsion field degree: | $20127744$ |
Rational points
This modular curve has 6 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 |
|---|---|---|---|---|---|
| 12.48.0-12.g.1.3 | $12$ | $2$ | $2$ | $0$ | $0$ |
| 312.48.0-12.g.1.17 | $312$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.