Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $600$ | ||
| Index: | $72$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 8 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
| Elliptic points: | $8$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12T1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.72.1.9 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}7&36\\21&17\end{bmatrix}$, $\begin{bmatrix}17&36\\18&47\end{bmatrix}$, $\begin{bmatrix}33&26\\25&33\end{bmatrix}$, $\begin{bmatrix}45&56\\26&33\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 60-isogeny field degree: | $24$ |
| Cyclic 60-torsion field degree: | $384$ |
| Full 60-torsion field degree: | $30720$ |
Jacobian
| Conductor: | $2^{3}\cdot3\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 600.2.a.h |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{sp}}^+(6)$ | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.36.0.f.1 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.36.1.es.1 | $60$ | $2$ | $2$ | $1$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| 60.144.5.b.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.cw.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.gh.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.144.5.gk.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.144.5.lu.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.md.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.mj.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.144.5.mm.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.360.25.cfm.1 | $60$ | $5$ | $5$ | $25$ | $6$ | $1^{24}$ |
| 60.432.25.bkg.1 | $60$ | $6$ | $6$ | $25$ | $3$ | $1^{24}$ |
| 60.720.49.ejw.1 | $60$ | $10$ | $10$ | $49$ | $8$ | $1^{48}$ |
| 120.144.5.ms.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.ue.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.bvv.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.bwq.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.dmd.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.dnt.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.dpj.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.dqe.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 180.216.9.bg.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 180.216.9.bs.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 180.216.9.cr.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |