Invariants
Level: | $120$ | $\SL_2$-level: | $24$ | 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: | $8$ (of which $4$ are rational) | Cusp widths | $1^{2}\cdot2\cdot3^{2}\cdot6\cdot8\cdot24$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
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: | 24G1 |
Level structure
$\GL_2(\Z/120\Z)$-generators: | $\begin{bmatrix}13&66\\106&89\end{bmatrix}$, $\begin{bmatrix}64&57\\73&56\end{bmatrix}$, $\begin{bmatrix}67&44\\112&87\end{bmatrix}$, $\begin{bmatrix}71&108\\98&97\end{bmatrix}$, $\begin{bmatrix}76&75\\85&2\end{bmatrix}$, $\begin{bmatrix}91&92\\106&105\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.48.1.zx.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 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 |
---|---|---|---|---|---|---|
24.48.0-12.g.1.12 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
120.24.0-120.z.1.32 | $120$ | $4$ | $4$ | $0$ | $?$ | full Jacobian |
120.48.0-12.g.1.7 | $120$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
120.192.1-120.rg.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rg.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rg.3.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.rg.4.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ri.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ri.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ri.3.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ri.4.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sq.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sq.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sq.3.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.sq.4.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ss.1.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ss.2.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ss.3.31 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.1-120.ss.4.32 | $120$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
120.192.3-120.fz.1.35 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.hs.1.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.jl.1.11 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.jm.1.10 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mc.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mf.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mh.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.mi.1.26 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.op.1.14 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.oq.1.22 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.os.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.ov.1.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.pn.1.39 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.po.1.27 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qc.1.20 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.qf.1.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sn.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sn.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sn.3.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sn.4.24 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sp.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sp.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sp.3.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.sp.4.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tl.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tl.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tl.3.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tl.4.28 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tn.1.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tn.2.32 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tn.3.31 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.192.3-120.tn.4.30 | $120$ | $2$ | $2$ | $3$ | $?$ | not computed |
120.288.5-120.bem.1.48 | $120$ | $3$ | $3$ | $5$ | $?$ | not computed |
120.480.17-120.brh.1.24 | $120$ | $5$ | $5$ | $17$ | $?$ | not computed |