Invariants
Level: | $140$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $160$ | $\PSL_2$-index: | $160$ | ||||
Genus: | $9 = 1 + \frac{ 160 }{12} - \frac{ 0 }{4} - \frac{ 4 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $20^{8}$ | Cusp orbits | $8$ | ||
Elliptic points: | $0$ of order $2$ and $4$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 16$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 9$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20A9 |
Level structure
$\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}46&7\\113&18\end{bmatrix}$, $\begin{bmatrix}61&43\\132&59\end{bmatrix}$, $\begin{bmatrix}80&87\\107&20\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 140-isogeny field degree: | $288$ |
Cyclic 140-torsion field degree: | $13824$ |
Full 140-torsion field degree: | $580608$ |
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 |
---|---|---|---|---|---|
20.80.3.b.1 | $20$ | $2$ | $2$ | $3$ | $2$ |
70.40.1.k.1 | $70$ | $4$ | $4$ | $1$ | $0$ |
140.80.5.c.1 | $140$ | $2$ | $2$ | $5$ | $?$ |
140.80.5.e.1 | $140$ | $2$ | $2$ | $5$ | $?$ |