Invariants
Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1200$ | ||
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: | $5$ | ||||||
$\Q$-gonality: | $4 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 8$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | yes $\quad(D =$ $-3$) |
Other labels
Cummins and Pauli (CP) label: | 60U15 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.15.1446 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}25&4\\6&5\end{bmatrix}$, $\begin{bmatrix}25&27\\48&55\end{bmatrix}$, $\begin{bmatrix}25&59\\24&17\end{bmatrix}$, $\begin{bmatrix}49&38\\48&13\end{bmatrix}$, $\begin{bmatrix}53&51\\18&7\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.240.15.gf.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: | $2^{35}\cdot3^{11}\cdot5^{30}$ |
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, 400.2.a.d$^{2}$, 1200.2.a.a, 1200.2.a.f, 1200.2.a.g, 1200.2.a.m, 1200.2.a.p, 1200.2.a.s |
Rational points
This modular curve has 1 rational CM point but no rational cusps or other 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.1.14 | $30$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
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.fg.1.1 | $60$ | $2$ | $2$ | $29$ | $7$ | $1^{14}$ |
60.960.29-60.fj.1.3 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.le.1.1 | $60$ | $2$ | $2$ | $29$ | $16$ | $1^{14}$ |
60.960.29-60.lg.1.3 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.oi.1.10 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.ok.1.3 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
60.960.29-60.pc.1.2 | $60$ | $2$ | $2$ | $29$ | $7$ | $1^{14}$ |
60.960.29-60.pe.1.3 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
60.960.33-60.bb.1.3 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.bp.1.18 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.kj.1.2 | $60$ | $2$ | $2$ | $33$ | $18$ | $1^{18}$ |
60.960.33-60.kl.1.10 | $60$ | $2$ | $2$ | $33$ | $17$ | $1^{18}$ |
60.960.33-60.nf.1.14 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.nh.1.10 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
60.960.33-60.nw.1.14 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
60.960.33-60.ny.1.10 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.rq.1.15 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{18}$ |
60.960.33-60.rs.1.11 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
60.960.33-60.sg.1.16 | $60$ | $2$ | $2$ | $33$ | $9$ | $1^{18}$ |
60.960.33-60.si.1.15 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.te.1.16 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.tg.1.16 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
60.960.33-60.tp.1.15 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
60.960.33-60.ts.1.20 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
60.1440.43-60.pu.1.23 | $60$ | $3$ | $3$ | $43$ | $9$ | $1^{28}$ |
60.1440.49-60.biu.1.13 | $60$ | $3$ | $3$ | $49$ | $16$ | $1^{32}\cdot2$ |