Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $300$ | ||
| Index: | $1920$ | $\PSL_2$-index: | $960$ | ||||
| Genus: | $61 = 1 + \frac{ 960 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 40 }{2}$ | ||||||
| Cusps: | $40$ (none of which are rational) | Cusp widths | $10^{16}\cdot20^{4}\cdot30^{16}\cdot60^{4}$ | Cusp orbits | $4^{4}\cdot8^{3}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $10 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $10 \le \gamma \le 20$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.1920.61.1314 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}15&32\\32&51\end{bmatrix}$, $\begin{bmatrix}17&4\\14&39\end{bmatrix}$, $\begin{bmatrix}27&14\\34&59\end{bmatrix}$, $\begin{bmatrix}31&56\\36&29\end{bmatrix}$, $\begin{bmatrix}37&38\\18&11\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.960.61.a.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $1152$ |
Jacobian
| Conductor: | $2^{90}\cdot3^{51}\cdot5^{122}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{29}\cdot4^{2}\cdot8^{3}$ |
| Newforms: | 50.2.a.a$^{4}$, 50.2.a.b$^{4}$, 75.2.a.a$^{3}$, 75.2.a.b$^{3}$, 75.2.a.c$^{3}$, 100.2.a.a$^{2}$, 150.2.a.a$^{2}$, 150.2.a.b$^{2}$, 150.2.a.c$^{2}$, 300.2.a.a, 300.2.a.b, 300.2.a.c, 300.2.a.d, 300.2.e.a, 300.2.e.b, 300.2.e.c, 300.2.e.d, 300.2.e.e |
Rational points
This modular curve has no real points and no $\Q_p$ points for $p=29,53$, 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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(5)$ | $5$ | $96$ | $48$ | $0$ | $0$ | full Jacobian |
| 12.96.0-12.a.2.9 | $12$ | $20$ | $20$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.960.29-30.a.1.7 | $60$ | $2$ | $2$ | $29$ | $1$ | $4^{2}\cdot8^{3}$ |
| 60.960.29-30.a.1.9 | $60$ | $2$ | $2$ | $29$ | $1$ | $4^{2}\cdot8^{3}$ |
| 60.960.31-60.a.2.7 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{14}\cdot4^{2}\cdot8$ |
| 60.960.31-60.a.2.59 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{14}\cdot4^{2}\cdot8$ |
| 60.960.31-60.d.1.26 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{14}\cdot8^{2}$ |
| 60.960.31-60.d.1.40 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{14}\cdot8^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.3840.129-60.a.1.6 | $60$ | $2$ | $2$ | $129$ | $14$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.a.1.11 | $60$ | $2$ | $2$ | $129$ | $14$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.b.1.2 | $60$ | $2$ | $2$ | $129$ | $7$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.b.3.11 | $60$ | $2$ | $2$ | $129$ | $7$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.e.1.16 | $60$ | $2$ | $2$ | $129$ | $19$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.e.2.1 | $60$ | $2$ | $2$ | $129$ | $19$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.f.1.7 | $60$ | $2$ | $2$ | $129$ | $13$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.f.2.11 | $60$ | $2$ | $2$ | $129$ | $13$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.bw.2.6 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.bw.4.15 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.bx.2.7 | $60$ | $2$ | $2$ | $129$ | $6$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.bx.4.10 | $60$ | $2$ | $2$ | $129$ | $6$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ca.1.9 | $60$ | $2$ | $2$ | $129$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.ca.2.8 | $60$ | $2$ | $2$ | $129$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cb.1.3 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.129-60.cb.3.11 | $60$ | $2$ | $2$ | $129$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ki.1.6 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.kj.1.4 | $60$ | $2$ | $2$ | $137$ | $6$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.km.2.1 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.kn.2.8 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.me.1.6 | $60$ | $2$ | $2$ | $137$ | $14$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.mf.1.4 | $60$ | $2$ | $2$ | $137$ | $7$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.mi.2.5 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.3840.137-60.mj.2.3 | $60$ | $2$ | $2$ | $137$ | $13$ | $1^{36}\cdot2^{10}\cdot4^{5}$ |
| 60.5760.181-60.m.2.18 | $60$ | $3$ | $3$ | $181$ | $3$ | $1^{56}\cdot4^{4}\cdot8^{6}$ |
| 60.5760.201-60.c.1.12 | $60$ | $3$ | $3$ | $201$ | $15$ | $1^{62}\cdot2^{7}\cdot4^{2}\cdot8^{7}$ |