Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (of which $2$ are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{2}\cdot2$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}41&120\\232&217\end{bmatrix}$, $\begin{bmatrix}74&85\\37&198\end{bmatrix}$, $\begin{bmatrix}86&211\\73&4\end{bmatrix}$, $\begin{bmatrix}95&38\\66&83\end{bmatrix}$, $\begin{bmatrix}193&140\\160&13\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 240.24.1.d.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $96$ |
Cyclic 240-torsion field degree: | $6144$ |
Full 240-torsion field degree: | $11796480$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0-8.o.1.6 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.24.0-8.o.1.2 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
240.96.1-240.b.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.e.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.n.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.p.1.21 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.du.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dx.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.dy.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.eb.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gw.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.gz.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ha.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hd.1.23 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ic.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.if.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ig.1.16 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ij.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.144.5-240.h.1.47 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
240.192.5-240.bwc.1.39 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |
240.240.9-240.h.1.26 | $240$ | $5$ | $5$ | $9$ | $?$ | not computed |
240.288.9-240.pr.1.43 | $240$ | $6$ | $6$ | $9$ | $?$ | not computed |
240.480.17-240.jp.1.34 | $240$ | $10$ | $10$ | $17$ | $?$ | not computed |