Invariants
Level: | $140$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot20^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20D5 |
Level structure
$\GL_2(\Z/140\Z)$-generators: | $\begin{bmatrix}23&115\\97&126\end{bmatrix}$, $\begin{bmatrix}102&79\\73&93\end{bmatrix}$, $\begin{bmatrix}103&73\\124&117\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 140.96.5.bw.1 for the level structure with $-I$) |
Cyclic 140-isogeny field degree: | $48$ |
Cyclic 140-torsion field degree: | $2304$ |
Full 140-torsion field degree: | $483840$ |
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 |
---|---|---|---|---|---|
20.96.3-20.i.2.6 | $20$ | $2$ | $2$ | $3$ | $0$ |
140.48.1-70.d.2.3 | $140$ | $4$ | $4$ | $1$ | $?$ |
140.96.3-20.i.2.4 | $140$ | $2$ | $2$ | $3$ | $?$ |