Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{16}\cdot16^{8}$ | Cusp orbits | $4^{6}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $3 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $3 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16M5 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}63&136\\218&155\end{bmatrix}$, $\begin{bmatrix}139&228\\124&49\end{bmatrix}$, $\begin{bmatrix}161&136\\42&29\end{bmatrix}$, $\begin{bmatrix}163&140\\64&129\end{bmatrix}$, $\begin{bmatrix}193&144\\78&113\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 240.384.5-240.uc.2.1, 240.384.5-240.uc.2.2, 240.384.5-240.uc.2.3, 240.384.5-240.uc.2.4, 240.384.5-240.uc.2.5, 240.384.5-240.uc.2.6, 240.384.5-240.uc.2.7, 240.384.5-240.uc.2.8, 240.384.5-240.uc.2.9, 240.384.5-240.uc.2.10, 240.384.5-240.uc.2.11, 240.384.5-240.uc.2.12, 240.384.5-240.uc.2.13, 240.384.5-240.uc.2.14, 240.384.5-240.uc.2.15, 240.384.5-240.uc.2.16 |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $2949120$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
24.96.1.cg.1 | $24$ | $2$ | $2$ | $1$ | $1$ |
80.96.3.dm.2 | $80$ | $2$ | $2$ | $3$ | $?$ |
240.96.1.n.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.1.r.1 | $240$ | $2$ | $2$ | $1$ | $?$ |
240.96.3.fr.1 | $240$ | $2$ | $2$ | $3$ | $?$ |
240.96.3.gh.2 | $240$ | $2$ | $2$ | $3$ | $?$ |
240.96.3.id.2 | $240$ | $2$ | $2$ | $3$ | $?$ |