Invariants
Level: | $60$ | $\SL_2$-level: | $12$ | Newform level: | $1200$ | ||
Index: | $384$ | $\PSL_2$-index: | $192$ | ||||
Genus: | $5 = 1 + \frac{ 192 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $4^{12}\cdot12^{12}$ | Cusp orbits | $2^{6}\cdot4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $1$ | ||||||
$\Q$-gonality: | $2 \le \gamma \le 4$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 4$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12E5 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.384.5.626 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}17&44\\42&53\end{bmatrix}$, $\begin{bmatrix}23&12\\18&43\end{bmatrix}$, $\begin{bmatrix}49&48\\0&31\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.192.5.r.3 for the level structure with $-I$) |
Cyclic 60-isogeny field degree: | $6$ |
Cyclic 60-torsion field degree: | $96$ |
Full 60-torsion field degree: | $5760$ |
Jacobian
Conductor: | $2^{18}\cdot3^{5}\cdot5^{4}$ |
Simple: | no |
Squarefree: | yes |
Decomposition: | $1^{3}\cdot2$ |
Newforms: | 24.2.a.a, 48.2.c.a, 600.2.a.h, 1200.2.a.d |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.192.3-12.g.2.5 | $12$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
60.192.1-60.b.3.3 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
60.192.1-60.b.3.10 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
60.192.1-60.e.2.3 | $60$ | $2$ | $2$ | $1$ | $1$ | $1^{2}\cdot2$ |
60.192.1-60.e.2.11 | $60$ | $2$ | $2$ | $1$ | $1$ | $1^{2}\cdot2$ |
60.192.1-60.f.4.3 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
60.192.1-60.f.4.11 | $60$ | $2$ | $2$ | $1$ | $0$ | $1^{2}\cdot2$ |
60.192.3-60.c.1.4 | $60$ | $2$ | $2$ | $3$ | $1$ | $2$ |
60.192.3-60.c.1.5 | $60$ | $2$ | $2$ | $3$ | $1$ | $2$ |
60.192.3-12.g.2.4 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
60.192.3-60.s.2.4 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
60.192.3-60.s.2.8 | $60$ | $2$ | $2$ | $3$ | $1$ | $1^{2}$ |
60.192.3-60.t.2.2 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
60.192.3-60.t.2.14 | $60$ | $2$ | $2$ | $3$ | $0$ | $1^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
60.1152.25-60.i.2.3 | $60$ | $3$ | $3$ | $25$ | $3$ | $1^{10}\cdot2^{5}$ |
60.1920.69-60.bl.2.1 | $60$ | $5$ | $5$ | $69$ | $6$ | $1^{32}\cdot2^{4}\cdot8^{3}$ |
60.2304.73-60.ex.2.3 | $60$ | $6$ | $6$ | $73$ | $6$ | $1^{34}\cdot2\cdot4^{2}\cdot8^{3}$ |
60.3840.137-60.jk.1.2 | $60$ | $10$ | $10$ | $137$ | $8$ | $1^{66}\cdot2^{5}\cdot4^{2}\cdot8^{6}$ |