Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $3600$ | ||
| Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
| Genus: | $13 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (of which $4$ are rational) | Cusp widths | $12^{24}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4^{2}\cdot8$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $3$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 6$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 6$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12A13 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.576.13.230 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&18\\54&25\end{bmatrix}$, $\begin{bmatrix}5&12\\12&5\end{bmatrix}$, $\begin{bmatrix}20&29\\33&40\end{bmatrix}$, $\begin{bmatrix}40&3\\51&52\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.288.13.fz.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $6$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $3840$ |
Jacobian
| Conductor: | $2^{45}\cdot3^{20}\cdot5^{16}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{13}$ |
| Newforms: | 36.2.a.a, 48.2.a.a$^{2}$, 144.2.a.a, 144.2.a.b, 600.2.a.h$^{2}$, 900.2.a.g, 1200.2.a.d$^{2}$, 1800.2.a.m, 3600.2.a.e, 3600.2.a.v |
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 |
|---|---|---|---|---|---|---|
| 12.288.5-12.n.1.4 | $12$ | $2$ | $2$ | $5$ | $0$ | $1^{8}$ |
| 60.192.3-60.bh.1.2 | $60$ | $3$ | $3$ | $3$ | $1$ | $1^{10}$ |
| 60.288.5-12.n.1.6 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{8}$ |
| 60.288.7-60.fu.1.3 | $60$ | $2$ | $2$ | $7$ | $1$ | $1^{6}$ |
| 60.288.7-60.fu.1.5 | $60$ | $2$ | $2$ | $7$ | $1$ | $1^{6}$ |
| 60.288.7-60.fw.1.2 | $60$ | $2$ | $2$ | $7$ | $2$ | $1^{6}$ |
| 60.288.7-60.fw.1.4 | $60$ | $2$ | $2$ | $7$ | $2$ | $1^{6}$ |
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.da.1.2 | $60$ | $2$ | $2$ | $25$ | $3$ | $2^{6}$ |
| 60.1152.25-60.da.1.5 | $60$ | $2$ | $2$ | $25$ | $3$ | $2^{6}$ |
| 60.1152.25-60.db.1.1 | $60$ | $2$ | $2$ | $25$ | $3$ | $2^{6}$ |
| 60.1152.25-60.db.1.6 | $60$ | $2$ | $2$ | $25$ | $3$ | $2^{6}$ |
| 60.2880.109-60.ccg.1.5 | $60$ | $5$ | $5$ | $109$ | $33$ | $1^{96}$ |
| 60.3456.121-60.coe.1.1 | $60$ | $6$ | $6$ | $121$ | $28$ | $1^{108}$ |
| 60.5760.217-60.coj.1.5 | $60$ | $10$ | $10$ | $217$ | $55$ | $1^{204}$ |