Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $1200$ | ||
| Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
| Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (of which $4$ are rational) | Cusp widths | $4^{12}\cdot12^{12}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
| $\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12E5 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.384.5.258 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}5&22\\36&7\end{bmatrix}$, $\begin{bmatrix}7&12\\0&47\end{bmatrix}$, $\begin{bmatrix}35&18\\6&43\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.192.5.h.2 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $6$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $5760$ |
Jacobian
| Conductor: | $2^{18}\cdot3^{5}\cdot5^{8}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1^{3}\cdot2$ |
| Newforms: | 24.2.a.a, 600.2.a.h, 1200.2.a.d, 1200.2.h.e |
Rational points
This modular curve has 4 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 |
|---|---|---|---|---|---|---|
| 12.192.1-12.b.1.3 | $12$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
| 60.192.1-12.b.1.5 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
| 60.192.1-60.e.3.7 | $60$ | $2$ | $2$ | $1$ | $1$ | $1^{2}\cdot2$ |
| 60.192.1-60.e.3.15 | $60$ | $2$ | $2$ | $1$ | $1$ | $1^{2}\cdot2$ |
| 60.192.1-60.f.4.3 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
| 60.192.1-60.f.4.9 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
| 60.192.3-60.c.1.4 | $60$ | $2$ | $2$ | $3$ | $1$ | $2$ |
| 60.192.3-60.c.1.9 | $60$ | $2$ | $2$ | $3$ | $1$ | $2$ |
| 60.192.3-60.l.1.7 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 60.192.3-60.l.1.13 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 60.192.3-60.o.1.4 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 60.192.3-60.o.1.6 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
| 60.192.3-60.p.1.1 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
| 60.192.3-60.p.1.13 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.1152.25-60.l.2.7 | $60$ | $3$ | $3$ | $25$ | $3$ | $1^{10}\cdot2^{5}$ |
| 60.1920.69-60.r.1.5 | $60$ | $5$ | $5$ | $69$ | $6$ | $1^{32}\cdot2^{4}\cdot8^{3}$ |
| 60.2304.73-60.bl.1.2 | $60$ | $6$ | $6$ | $73$ | $6$ | $1^{34}\cdot2\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ck.3.4 | $60$ | $10$ | $10$ | $137$ | $8$ | $1^{66}\cdot2^{5}\cdot4^{2}\cdot8^{6}$ |