Invariants
| Level: | $60$ | $\SL_2$-level: | $20$ | 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 | $2^{6}\cdot10^{6}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
| Elliptic points: | $0$ 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: | 10K1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.144.1.263 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}3&50\\20&31\end{bmatrix}$, $\begin{bmatrix}17&45\\34&1\end{bmatrix}$, $\begin{bmatrix}23&40\\20&9\end{bmatrix}$, $\begin{bmatrix}43&0\\26&59\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.72.1.cf.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $8$ |
| Cyclic 60-torsion field degree: | $64$ |
| Full 60-torsion field degree: | $15360$ |
Jacobian
| Conductor: | $2^{4}\cdot3^{2}\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 3600.2.a.be |
Rational points
This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 20.72.0-10.a.2.4 | $20$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.72.0-10.a.2.9 | $60$ | $2$ | $2$ | $0$ | $0$ | 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.fq.1.2 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.fu.1.10 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.kp.1.6 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.kv.1.6 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 60.288.5-60.pa.1.1 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 60.288.5-60.pg.1.5 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.288.5-60.qa.1.5 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 60.288.5-60.qe.1.5 | $60$ | $2$ | $2$ | $5$ | $2$ | $1^{2}\cdot2$ |
| 60.432.13-60.gn.2.25 | $60$ | $3$ | $3$ | $13$ | $1$ | $1^{6}\cdot2^{3}$ |
| 60.576.13-60.nr.2.27 | $60$ | $4$ | $4$ | $13$ | $4$ | $1^{6}\cdot2^{3}$ |
| 60.720.13-60.bu.1.7 | $60$ | $5$ | $5$ | $13$ | $3$ | $1^{6}\cdot2^{3}$ |
| 120.288.5-120.bor.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.bpt.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.ddf.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.dev.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.egs.1.8 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.eii.1.4 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.enq.1.14 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.288.5-120.eos.1.6 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |