Invariants
| Level: | $60$ | $\SL_2$-level: | $20$ | Newform level: | $3600$ | ||
| Index: | $240$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $15 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
| Cusps: | $12$ (none of which are rational) | Cusp widths | $20^{12}$ | Cusp orbits | $4^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $3$ | ||||||
| $\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
| $\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 20D15 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.240.15.101 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}5&54\\7&59\end{bmatrix}$, $\begin{bmatrix}9&44\\47&3\end{bmatrix}$, $\begin{bmatrix}43&2\\52&37\end{bmatrix}$, $\begin{bmatrix}51&4\\4&59\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 60-isogeny field degree: | $48$ |
| Cyclic 60-torsion field degree: | $768$ |
| Full 60-torsion field degree: | $9216$ |
Jacobian
| Conductor: | $2^{38}\cdot3^{16}\cdot5^{26}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{15}$ |
| Newforms: | 50.2.a.b$^{2}$, 100.2.a.a, 180.2.a.a$^{2}$, 200.2.a.c, 200.2.a.e, 360.2.a.a, 400.2.a.a, 400.2.a.e, 450.2.a.g$^{2}$, 720.2.a.h, 1800.2.a.r, 3600.2.a.l |
Rational points
This modular curve has no $\Q_p$ points for $p=17$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 20.120.7.cr.1 | $20$ | $2$ | $2$ | $7$ | $2$ | $1^{8}$ |
| 60.24.0.z.1 | $60$ | $10$ | $10$ | $0$ | $0$ | full Jacobian |
| 60.120.7.fw.1 | $60$ | $2$ | $2$ | $7$ | $2$ | $1^{8}$ |
| 60.120.7.jx.1 | $60$ | $2$ | $2$ | $7$ | $3$ | $1^{8}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.480.29.qt.1 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
| 60.480.29.qx.1 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
| 60.480.29.rj.1 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
| 60.480.29.rn.1 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
| 60.480.29.tf.1 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
| 60.480.29.tj.1 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
| 60.480.29.tv.1 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
| 60.480.29.tz.1 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
| 60.720.43.vt.1 | $60$ | $3$ | $3$ | $43$ | $11$ | $1^{28}$ |
| 60.720.55.bno.1 | $60$ | $3$ | $3$ | $55$ | $20$ | $1^{40}$ |
| 60.960.69.pq.1 | $60$ | $4$ | $4$ | $69$ | $14$ | $1^{54}$ |