Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $900$ | ||
| 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 | $3^{8}\cdot12^{4}$ | 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: | 12S1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.144.1.149 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}4&33\\51&4\end{bmatrix}$, $\begin{bmatrix}11&56\\18&49\end{bmatrix}$, $\begin{bmatrix}31&22\\6&5\end{bmatrix}$, $\begin{bmatrix}38&9\\21&32\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.72.1.s.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: | $2^{2}\cdot3^{2}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 900.2.a.g |
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.q.1.7 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.48.0-60.q.1.8 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.72.0-6.a.1.4 | $60$ | $2$ | $2$ | $0$ | $0$ | 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.b.1.5 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.ci.1.2 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.hd.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.hg.1.3 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.ja.1.2 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.jg.1.4 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.jw.1.7 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.kb.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.720.25-60.mf.1.8 | $60$ | $5$ | $5$ | $25$ | $4$ | $1^{24}$ |
| 60.864.25-60.gt.1.16 | $60$ | $6$ | $6$ | $25$ | $2$ | $1^{24}$ |
| 60.1440.49-60.bay.1.14 | $60$ | $10$ | $10$ | $49$ | $5$ | $1^{48}$ |
| 120.288.5-120.gf.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.qh.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cfg.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cgb.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.csk.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cua.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cyj.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.czs.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 180.432.7-180.s.1.8 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.s.1.10 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.ba.1.8 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-180.bh.1.6 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.10-180.e.1.8 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.10-180.e.1.10 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.13-180.bh.1.8 | $180$ | $3$ | $3$ | $13$ | $?$ | not computed |