Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $3600$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $10^{2}\cdot20^{2}\cdot30^{2}\cdot60^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $4$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
| Rational cusps: | $4$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 60B17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.17.956 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}11&45\\12&13\end{bmatrix}$, $\begin{bmatrix}23&44\\12&5\end{bmatrix}$, $\begin{bmatrix}35&28\\36&55\end{bmatrix}$, $\begin{bmatrix}53&57\\36&1\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.17.bb.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $6$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $4608$ |
Jacobian
| Conductor: | $2^{42}\cdot3^{22}\cdot5^{34}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{17}$ |
| Newforms: | 50.2.a.b$^{4}$, 75.2.a.a$^{3}$, 300.2.a.b, 3600.2.a.bk, 3600.2.a.bq, 3600.2.a.i, 3600.2.a.l$^{2}$, 3600.2.a.m$^{2}$, 3600.2.a.v, 3600.2.a.z |
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 |
|---|---|---|---|---|---|---|
| 60.96.1-60.p.1.3 | $60$ | $5$ | $5$ | $1$ | $0$ | $1^{16}$ |
| 60.120.4-60.p.1.4 | $60$ | $4$ | $4$ | $4$ | $1$ | $1^{13}$ |
| 60.240.8-60.o.1.5 | $60$ | $2$ | $2$ | $8$ | $0$ | $1^{9}$ |
| 60.240.8-60.o.1.11 | $60$ | $2$ | $2$ | $8$ | $0$ | $1^{9}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.960.33-60.cf.1.4 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.1.6 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.2.3 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.2.5 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.3.4 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.3.6 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.4.3 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.960.33-60.cf.4.5 | $60$ | $2$ | $2$ | $33$ | $4$ | $8^{2}$ |
| 60.1440.49-60.gp.1.4 | $60$ | $3$ | $3$ | $49$ | $10$ | $1^{32}$ |
| 60.1440.53-60.bjo.1.5 | $60$ | $3$ | $3$ | $53$ | $16$ | $1^{36}$ |
| 60.1920.65-60.ko.1.4 | $60$ | $4$ | $4$ | $65$ | $17$ | $1^{48}$ |