Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $1800$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $9 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 32 }{2}$ | ||||||
| Cusps: | $32$ (of which $2$ are rational) | Cusp widths | $6^{16}\cdot12^{16}$ | Cusp orbits | $1^{2}\cdot2^{5}\cdot4^{3}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 6$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12B9 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.576.9.121 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}5&56\\48&55\end{bmatrix}$, $\begin{bmatrix}17&18\\24&17\end{bmatrix}$, $\begin{bmatrix}37&46\\6&41\end{bmatrix}$, $\begin{bmatrix}47&2\\36&55\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.288.9.d.2 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $3840$ |
Jacobian
| Conductor: | $2^{21}\cdot3^{16}\cdot5^{12}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{5}\cdot2^{2}$ |
| Newforms: | 36.2.a.a, 36.2.b.a, 600.2.a.h$^{2}$, 900.2.a.g, 900.2.e.b, 1800.2.a.m |
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 |
|---|---|---|---|---|---|---|
| 12.288.3-12.a.1.13 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{4}\cdot2$ |
| 60.192.1-60.f.3.6 | $60$ | $3$ | $3$ | $1$ | $0$ | $1^{4}\cdot2^{2}$ |
| 60.192.1-60.f.4.3 | $60$ | $3$ | $3$ | $1$ | $0$ | $1^{4}\cdot2^{2}$ |
| 60.288.3-12.a.1.11 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{4}\cdot2$ |
| 60.288.3-60.a.1.14 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{4}\cdot2$ |
| 60.288.3-60.a.1.17 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{4}\cdot2$ |
| 60.288.5-60.b.1.3 | $60$ | $2$ | $2$ | $5$ | $1$ | $2^{2}$ |
| 60.288.5-60.b.1.6 | $60$ | $2$ | $2$ | $5$ | $1$ | $2^{2}$ |
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.h.1.7 | $60$ | $2$ | $2$ | $25$ | $2$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.i.2.3 | $60$ | $2$ | $2$ | $25$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.k.1.2 | $60$ | $2$ | $2$ | $25$ | $2$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.l.2.7 | $60$ | $2$ | $2$ | $25$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.bi.2.2 | $60$ | $2$ | $2$ | $25$ | $2$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.bk.2.6 | $60$ | $2$ | $2$ | $25$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.bm.1.8 | $60$ | $2$ | $2$ | $25$ | $2$ | $1^{8}\cdot2^{4}$ |
| 60.1152.25-60.bo.2.4 | $60$ | $2$ | $2$ | $25$ | $3$ | $1^{8}\cdot2^{4}$ |
| 60.2880.105-60.f.1.13 | $60$ | $5$ | $5$ | $105$ | $11$ | $1^{48}\cdot8^{6}$ |
| 60.3456.113-60.bt.2.14 | $60$ | $6$ | $6$ | $113$ | $8$ | $1^{52}\cdot2^{2}\cdot8^{6}$ |
| 60.5760.209-60.cx.1.3 | $60$ | $10$ | $10$ | $209$ | $15$ | $1^{100}\cdot2^{2}\cdot8^{12}$ |