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 | $6^{12}$ | 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: | 60.144.1.145 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}8&15\\21&26\end{bmatrix}$, $\begin{bmatrix}10&39\\27&10\end{bmatrix}$, $\begin{bmatrix}49&18\\6&31\end{bmatrix}$, $\begin{bmatrix}52&37\\9&8\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 30.72.1.c.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 |
| 60.48.0-30.a.1.2 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.48.0-30.a.1.8 | $60$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
| 60.72.0-6.a.1.2 | $60$ | $2$ | $2$ | $0$ | $0$ | 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.ds.1.4 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.dw.1.7 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.gu.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.gw.1.4 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.iq.1.4 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{4}$ |
| 60.288.5-60.is.1.3 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{4}$ |
| 60.288.5-60.jw.1.7 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.288.5-60.ka.1.1 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}$ |
| 60.720.25-30.cf.1.3 | $60$ | $5$ | $5$ | $25$ | $4$ | $1^{24}$ |
| 60.864.25-30.n.1.6 | $60$ | $6$ | $6$ | $25$ | $2$ | $1^{24}$ |
| 60.1440.49-30.cu.1.12 | $60$ | $10$ | $10$ | $49$ | $5$ | $1^{48}$ |
| 120.288.5-120.zz.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.bbb.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.ccv.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cdj.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cps.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cqg.1.7 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.cyi.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.czk.1.3 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 180.432.7-90.e.1.4 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-90.e.1.12 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-90.g.1.6 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.7-90.h.1.4 | $180$ | $3$ | $3$ | $7$ | $?$ | not computed |
| 180.432.10-90.c.1.5 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.10-90.c.1.9 | $180$ | $3$ | $3$ | $10$ | $?$ | not computed |
| 180.432.13-90.r.1.5 | $180$ | $3$ | $3$ | $13$ | $?$ | not computed |