Invariants
Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $3600$ | ||
Index: | $480$ | $\PSL_2$-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 | $5^{4}\cdot15^{4}\cdot20^{2}\cdot60^{2}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $4$ | ||||||
$\Q$-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: | 60U15 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.15.1374 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}5&4\\36&55\end{bmatrix}$, $\begin{bmatrix}16&39\\9&14\end{bmatrix}$, $\begin{bmatrix}19&2\\36&11\end{bmatrix}$, $\begin{bmatrix}49&52\\6&11\end{bmatrix}$, $\begin{bmatrix}59&46\\6&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.240.15.fv.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: | $2^{35}\cdot3^{21}\cdot5^{30}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{15}$ |
Newforms: | 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 75.2.a.b$^{2}$, 150.2.a.b, 3600.2.a.bc$^{2}$, 3600.2.a.bg, 3600.2.a.bm, 3600.2.a.d, 3600.2.a.j, 3600.2.a.o, 3600.2.a.s |
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 |
---|---|---|---|---|---|---|
30.240.7-30.h.1.13 | $30$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
60.240.7-30.h.1.14 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
60.960.29-60.fs.1.1 | $60$ | $2$ | $2$ | $29$ | $7$ | $1^{14}$ |
60.960.29-60.fv.1.2 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.jc.1.3 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.960.29-60.jf.1.2 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.nc.1.4 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
60.960.29-60.nf.1.2 | $60$ | $2$ | $2$ | $29$ | $4$ | $1^{14}$ |
60.960.29-60.nj.1.2 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
60.960.29-60.nm.1.2 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.33-60.v.1.12 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.bm.1.20 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.ic.1.8 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.if.1.12 | $60$ | $2$ | $2$ | $33$ | $15$ | $1^{18}$ |
60.960.33-60.ly.1.14 | $60$ | $2$ | $2$ | $33$ | $14$ | $1^{18}$ |
60.960.33-60.mb.1.12 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
60.960.33-60.mg.1.14 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.mj.1.12 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.rt.1.13 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{18}$ |
60.960.33-60.rw.1.14 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.sb.1.14 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
60.960.33-60.se.1.15 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.sr.1.14 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.su.1.16 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
60.960.33-60.sv.1.13 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.sy.1.24 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
60.1440.43-60.pr.1.19 | $60$ | $3$ | $3$ | $43$ | $9$ | $1^{28}$ |
60.1440.49-60.bej.1.9 | $60$ | $3$ | $3$ | $49$ | $15$ | $1^{32}\cdot2$ |