Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $3600$ | ||
| Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
| Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ 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: | 6F1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.144.1.147 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}5&54\\24&53\end{bmatrix}$, $\begin{bmatrix}10&9\\9&10\end{bmatrix}$, $\begin{bmatrix}16&27\\9&16\end{bmatrix}$, $\begin{bmatrix}19&40\\12&17\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.72.1.o.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $192$ |
| Full 60-torsion field degree: | $15360$ |
Jacobian
| Conductor: | $2^{4}\cdot3^{2}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 3600.2.a.e |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.72.0-6.a.1.5 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.48.0-60.o.1.11 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.48.0-60.o.1.12 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.72.0-6.a.1.3 | $60$ | $2$ | $2$ | $0$ | $0$ | 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 |
|---|---|---|---|---|---|---|
| 60.288.5-60.dt.1.2 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.dx.1.3 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.gv.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.gy.1.2 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.ir.1.2 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.iu.1.2 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.jx.1.2 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.kb.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.720.25-60.mb.1.6 | $60$ | $5$ | $5$ | $25$ | $9$ | $1^{24}$ |
| 60.864.25-60.gp.1.14 | $60$ | $6$ | $6$ | $25$ | $5$ | $1^{24}$ |
| 60.1440.49-60.bau.1.11 | $60$ | $10$ | $10$ | $49$ | $12$ | $1^{48}$ |
| 120.288.5-120.bag.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.bbi.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cdc.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cdx.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cpz.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cqu.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cyp.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.czr.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 180.432.7-180.q.1.3 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.q.1.14 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.w.1.8 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.bd.1.4 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.10-180.c.1.10 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.10-180.c.1.15 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.13-180.bd.1.3 | $180$ | $3$ | $3$ | $13$ | $?$ | not computed |