Invariants
| Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $600$ | ||
| Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
| Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
| Cusps: | $16$ (of which $2$ are rational) | Cusp widths | $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $0$ | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 12V1 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.192.1.21 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}37&26\\18&13\end{bmatrix}$, $\begin{bmatrix}41&22\\48&7\end{bmatrix}$, $\begin{bmatrix}41&24\\12&37\end{bmatrix}$, $\begin{bmatrix}53&12\\18&13\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.96.1.f.4 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $11520$ |
Jacobian
| Conductor: | $2^{3}\cdot3\cdot5^{2}$ |
| Simple: | yes |
| Squarefree: | yes |
| Decomposition: | $1$ |
| Newforms: | 600.2.a.h |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal 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 |
|---|---|---|---|---|---|---|
| 3.8.0-3.a.1.1 | $3$ | $24$ | $24$ | $0$ | $0$ | full Jacobian |
| 20.24.0-20.b.1.2 | $20$ | $8$ | $8$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 12.96.0-12.a.2.15 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.96.0-12.a.2.12 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.96.0-60.a.1.16 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.96.0-60.a.1.28 | $60$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
| 60.96.1-60.b.1.1 | $60$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
| 60.96.1-60.b.1.18 | $60$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.384.5-60.g.1.5 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.384.5-60.h.2.8 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.384.5-60.m.2.5 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.384.5-60.o.2.8 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.384.5-60.q.2.8 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.384.5-60.r.3.6 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.384.5-60.w.3.8 | $60$ | $2$ | $2$ | $5$ | $1$ | $1^{2}\cdot2$ |
| 60.384.5-60.y.2.6 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{2}\cdot2$ |
| 60.576.9-60.d.2.2 | $60$ | $3$ | $3$ | $9$ | $1$ | $1^{4}\cdot2^{2}$ |
| 60.960.33-60.j.3.4 | $60$ | $5$ | $5$ | $33$ | $1$ | $1^{16}\cdot8^{2}$ |
| 60.1152.33-60.j.4.4 | $60$ | $6$ | $6$ | $33$ | $1$ | $1^{16}\cdot8^{2}$ |
| 60.1920.65-60.j.1.8 | $60$ | $10$ | $10$ | $65$ | $1$ | $1^{32}\cdot8^{4}$ |
| 120.384.5-120.iu.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ja.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ke.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.ks.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.og.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.om.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.pq.2.15 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |
| 120.384.5-120.qe.3.10 | $120$ | $2$ | $2$ | $5$ | $?$ | not computed |