Invariants
| Level: | $310$ | $\SL_2$-level: | $62$ | Newform level: | $1$ | ||
| Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $14 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
| Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $2^{3}\cdot62^{3}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 14$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 14$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 62B14 |
Level structure
| $\GL_2(\Z/310\Z)$-generators: | $\begin{bmatrix}54&243\\93&28\end{bmatrix}$, $\begin{bmatrix}70&57\\309&12\end{bmatrix}$, $\begin{bmatrix}306&155\\193&158\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 310.384.14-310.c.1.1, 310.384.14-310.c.1.2, 310.384.14-310.c.1.3, 310.384.14-310.c.1.4 |
| Cyclic 310-isogeny field degree: | $6$ |
| Cyclic 310-torsion field degree: | $720$ |
| Full 310-torsion field degree: | $13392000$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.6.0.a.1 | $10$ | $32$ | $32$ | $0$ | $0$ |
| $X_0(31)$ | $31$ | $6$ | $6$ | $2$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.6.0.a.1 | $10$ | $32$ | $32$ | $0$ | $0$ |
| $X_0(62)$ | $62$ | $2$ | $2$ | $7$ | $0$ |
| 310.64.4.a.1 | $310$ | $3$ | $3$ | $4$ | $?$ |