Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $1800$ | ||
| 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: | $1$ | ||||||
| $\Q$-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: | 60.72.1.68 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}27&2\\5&21\end{bmatrix}$, $\begin{bmatrix}39&10\\40&39\end{bmatrix}$, $\begin{bmatrix}39&34\\35&39\end{bmatrix}$, $\begin{bmatrix}45&26\\19&27\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $192$ |
| Full 60-torsion field degree: | $30720$ |
Jacobian
| Conductor: | $2^{3}\cdot3^{2}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 1800.2.a.m |
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
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 |
|---|---|---|---|---|---|---|
| 12.36.0.b.1 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 30.36.0.d.1 | $30$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.36.1.ek.1 | $60$ | $2$ | $2$ | $1$ | $1$ | 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 |
|---|---|---|---|---|---|---|
| 60.144.5.u.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.ch.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.el.1 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.144.5.en.1 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.144.5.iq.1 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.144.5.iv.1 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.144.5.iz.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.144.5.ji.1 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.360.25.cez.1 | $60$ | $5$ | $5$ | $25$ | $7$ | $1^{24}$ |
| 60.432.25.bjt.1 | $60$ | $6$ | $6$ | $25$ | $5$ | $1^{24}$ |
| 60.720.49.ejj.1 | $60$ | $10$ | $10$ | $49$ | $11$ | $1^{48}$ |
| 120.144.5.mf.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.qd.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.bgl.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.bgz.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.cpy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.crh.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.csj.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.144.5.cuy.1 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 180.216.9.l.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 180.216.9.t.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |
| 180.216.9.ce.1 | $180$ | $3$ | $3$ | $9$ | $?$ | not computed |