Invariants
| Level: | $140$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
| Index: | $60$ | $\PSL_2$-index: | $60$ | ||||
| Genus: | $4 = 1 + \frac{ 60 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
| Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $10^{2}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $3 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $3 \le \gamma \le 4$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20A4 |
Level structure
| $\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}3&54\\90&7\end{bmatrix}$, $\begin{bmatrix}65&6\\64&39\end{bmatrix}$, $\begin{bmatrix}77&118\\6&123\end{bmatrix}$, $\begin{bmatrix}89&90\\108&53\end{bmatrix}$, $\begin{bmatrix}139&10\\0&59\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | 140.120.4-140.b.1.1, 140.120.4-140.b.1.2, 140.120.4-140.b.1.3, 140.120.4-140.b.1.4, 140.120.4-140.b.1.5, 140.120.4-140.b.1.6, 140.120.4-140.b.1.7, 140.120.4-140.b.1.8, 280.120.4-140.b.1.1, 280.120.4-140.b.1.2, 280.120.4-140.b.1.3, 280.120.4-140.b.1.4, 280.120.4-140.b.1.5, 280.120.4-140.b.1.6, 280.120.4-140.b.1.7, 280.120.4-140.b.1.8 |
| Cyclic 140-isogeny field degree: | $96$ |
| Cyclic 140-torsion field degree: | $4608$ |
| Full 140-torsion field degree: | $1548288$ |
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 |
|---|---|---|---|---|---|
| $X_{S_4}(5)$ | $5$ | $12$ | $12$ | $0$ | $0$ |
| 28.12.0.b.1 | $28$ | $5$ | $5$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 10.30.2.a.1 | $10$ | $2$ | $2$ | $2$ | $0$ |
| 28.12.0.b.1 | $28$ | $5$ | $5$ | $0$ | $0$ |
| 140.30.2.c.1 | $140$ | $2$ | $2$ | $2$ | $?$ |
| 140.30.2.k.1 | $140$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 140.120.8.b.1 | $140$ | $2$ | $2$ | $8$ |
| 140.120.8.c.1 | $140$ | $2$ | $2$ | $8$ |
| 140.120.8.h.1 | $140$ | $2$ | $2$ | $8$ |
| 140.120.8.j.1 | $140$ | $2$ | $2$ | $8$ |
| 140.180.10.b.1 | $140$ | $3$ | $3$ | $10$ |
| 140.240.13.j.1 | $140$ | $4$ | $4$ | $13$ |
| 280.120.8.d.1 | $280$ | $2$ | $2$ | $8$ |
| 280.120.8.g.1 | $280$ | $2$ | $2$ | $8$ |
| 280.120.8.s.1 | $280$ | $2$ | $2$ | $8$ |
| 280.120.8.y.1 | $280$ | $2$ | $2$ | $8$ |