Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 48$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8F1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}53&0\\0&1\end{bmatrix}$, $\begin{bmatrix}71&32\\80&91\end{bmatrix}$, $\begin{bmatrix}89&72\\60&73\end{bmatrix}$, $\begin{bmatrix}97&88\\54&85\end{bmatrix}$, $\begin{bmatrix}103&76\\17&93\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 120.96.1-120.oq.1.1, 120.96.1-120.oq.1.2, 120.96.1-120.oq.1.3, 120.96.1-120.oq.1.4, 120.96.1-120.oq.1.5, 120.96.1-120.oq.1.6, 120.96.1-120.oq.1.7, 120.96.1-120.oq.1.8, 240.96.1-120.oq.1.1, 240.96.1-120.oq.1.2, 240.96.1-120.oq.1.3, 240.96.1-120.oq.1.4 |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $1536$ |
Full 120-torsion field degree: | $737280$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
8.24.0.w.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
60.24.0.h.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0.le.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.24.0.lf.1 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.24.1.m.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.24.1.nw.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.24.1.nx.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
120.144.9.ecg.1 | $120$ | $3$ | $3$ | $9$ | $?$ | not computed |
120.192.9.blk.1 | $120$ | $4$ | $4$ | $9$ | $?$ | not computed |
120.240.17.wo.1 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |
120.288.17.ula.1 | $120$ | $6$ | $6$ | $17$ | $?$ | not computed |
240.96.3.bex.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.96.3.bfa.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.96.3.bfb.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |
240.96.3.bfc.1 | $240$ | $2$ | $2$ | $3$ | $?$ | not computed |