Invariants
Level: | $120$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8K1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&68\\116&87\end{bmatrix}$, $\begin{bmatrix}33&68\\116&113\end{bmatrix}$, $\begin{bmatrix}53&8\\32&81\end{bmatrix}$, $\begin{bmatrix}73&100\\64&23\end{bmatrix}$, $\begin{bmatrix}113&68\\32&63\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.cz.2 for the level structure with $-I$) |
Cyclic 120-isogeny field degree: | $48$ |
Cyclic 120-torsion field degree: | $768$ |
Full 120-torsion field degree: | $184320$ |
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 |
---|---|---|---|---|---|---|
8.96.0-8.c.1.10 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.96.0-120.b.1.23 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.b.1.48 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-8.c.1.3 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cc.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.cc.2.32 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ce.2.4 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.0-120.ce.2.28 | $120$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
120.96.1-120.o.2.1 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.o.2.28 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dx.1.16 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dx.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dz.1.4 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.96.1-120.dz.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.384.5-120.hf.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hg.1.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hi.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hj.1.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hm.1.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hn.1.12 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hr.1.16 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
120.384.5-120.hv.3.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.n.2.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.t.2.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.v.2.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.bb.2.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.dl.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.dn.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.eb.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ed.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.nw.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ny.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.om.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.oo.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.qy.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.re.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.rg.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.rm.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |