Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $600$ | ||
| Index: | $480$ | $\PSL_2$-index: | $240$ | ||||
| Genus: | $17 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
| Cusps: | $8$ (none of which are rational) | Cusp widths | $10^{2}\cdot20^{2}\cdot30^{2}\cdot60^{2}$ | Cusp orbits | $2^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $2$ | ||||||
| $\Q$-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: | 60G17 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.17.42 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&50\\3&29\end{bmatrix}$, $\begin{bmatrix}11&36\\36&29\end{bmatrix}$, $\begin{bmatrix}17&46\\51&5\end{bmatrix}$, $\begin{bmatrix}29&18\\33&43\end{bmatrix}$, $\begin{bmatrix}55&18\\57&25\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.240.17.ng.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $192$ |
| Full 60-torsion field degree: | $4608$ |
Jacobian
| Conductor: | $2^{33}\cdot3^{11}\cdot5^{32}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{17}$ |
| Newforms: | 24.2.a.a, 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 150.2.a.b, 200.2.a.c$^{2}$, 200.2.a.e$^{2}$, 600.2.a.a, 600.2.a.b, 600.2.a.c, 600.2.a.e, 600.2.a.h |
Rational points
This modular curve has no $\Q_p$ points for $p=7$, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(5)$ | $5$ | $48$ | $24$ | $0$ | $0$ | full Jacobian |
| 12.48.1-12.k.1.2 | $12$ | $10$ | $10$ | $1$ | $0$ | $1^{16}$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.48.1-12.k.1.2 | $12$ | $10$ | $10$ | $1$ | $0$ | $1^{16}$ |
| 60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
| 60.240.7-30.h.1.23 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{10}$ |
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.n.1.42 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{16}$ |
| 60.960.33-60.bc.1.20 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.lm.1.14 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.ln.1.11 | $60$ | $2$ | $2$ | $33$ | $18$ | $1^{16}$ |
| 60.960.33-60.on.1.20 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{16}$ |
| 60.960.33-60.oo.1.13 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.or.1.11 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.os.1.14 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.qj.1.11 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{16}$ |
| 60.960.33-60.qk.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.qn.1.11 | $60$ | $2$ | $2$ | $33$ | $9$ | $1^{16}$ |
| 60.960.33-60.qo.1.10 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.qz.1.5 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{16}$ |
| 60.960.33-60.ra.1.11 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.rd.1.11 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{16}$ |
| 60.960.33-60.re.1.15 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.sv.1.13 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{16}$ |
| 60.960.33-60.sw.1.15 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.sz.1.10 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{16}$ |
| 60.960.33-60.ta.1.14 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.960.33-60.tl.1.12 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{16}$ |
| 60.960.33-60.tm.1.13 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{16}$ |
| 60.960.33-60.tp.1.15 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{16}$ |
| 60.960.33-60.tq.1.10 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{16}$ |
| 60.1440.49-60.bxr.1.14 | $60$ | $3$ | $3$ | $49$ | $6$ | $1^{32}$ |
| 60.1440.53-60.ebg.1.5 | $60$ | $3$ | $3$ | $53$ | $12$ | $1^{36}$ |