Invariants
Level: | $120$ | $\SL_2$-level: | $15$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-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 | $1^{2}\cdot3^{2}\cdot5^{2}\cdot15^{2}$ | Cusp orbits | $2^{4}$ | ||
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: | 15G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}5&57\\27&80\end{bmatrix}$, $\begin{bmatrix}8&3\\95&16\end{bmatrix}$, $\begin{bmatrix}41&73\\102&7\end{bmatrix}$, $\begin{bmatrix}68&103\\17&54\end{bmatrix}$, $\begin{bmatrix}110&51\\17&4\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.cah.1 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $12$ |
Cyclic 120-torsion field degree: | $384$ |
Full 120-torsion field degree: | $368640$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 | Kernel decomposition |
---|---|---|---|---|---|---|
15.48.1-15.a.1.5 | $15$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
120.48.1-15.a.1.3 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.5-120.el.1.18 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.en.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.er.2.17 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.et.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.hz.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.ib.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.if.2.9 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.ih.2.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.nf.1.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.nh.1.13 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.nl.1.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.nn.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.od.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.of.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.oj.1.11 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.192.5-120.ol.1.5 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.288.5-120.dap.1.13 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.288.5-120.ebh.1.38 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.384.13-120.fl.1.17 | $120$ | $4$ | $4$ | $13$ | $?$ | not computed |
120.480.9-120.b.1.25 | $120$ | $5$ | $5$ | $9$ | $?$ | not computed |
240.192.1-240.bfd.1.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfd.3.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfe.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfe.3.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bff.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bff.3.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfg.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfg.3.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfh.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfh.4.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfi.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfi.4.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfj.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfj.4.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfk.3.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.1-240.bfk.4.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.192.5-240.dgl.3.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgl.4.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgm.3.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgm.4.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgn.3.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgn.4.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgo.3.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgo.4.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgp.1.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgp.2.26 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgq.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgq.2.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgr.1.21 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgr.2.22 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgs.1.19 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.192.5-240.dgs.2.20 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |