Invariants
Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $900$ | ||
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 | $10^{6}\cdot30^{6}$ | Cusp orbits | $2^{2}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $2$ | ||||||
$\Q$-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: | 30E15 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.480.15.2018 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}13&50\\36&17\end{bmatrix}$, $\begin{bmatrix}37&36\\6&59\end{bmatrix}$, $\begin{bmatrix}41&42\\12&35\end{bmatrix}$, $\begin{bmatrix}58&41\\51&20\end{bmatrix}$, $\begin{bmatrix}58&45\\21&22\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 30.240.15.w.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: | $2^{13}\cdot3^{21}\cdot5^{30}$ |
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, 225.2.a.e, 450.2.a.b, 450.2.a.c$^{2}$, 450.2.a.f, 900.2.a.a, 900.2.a.e, 900.2.a.h |
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 |
---|---|---|---|---|---|---|
60.240.7-30.h.1.4 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{8}$ |
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 |
---|---|---|---|---|---|---|
60.960.29-30.d.1.15 | $60$ | $2$ | $2$ | $29$ | $3$ | $1^{14}$ |
60.960.29-30.l.1.6 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
60.960.29-30.x.1.9 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
60.960.29-30.y.1.9 | $60$ | $2$ | $2$ | $29$ | $3$ | $1^{14}$ |
60.960.29-60.ee.1.15 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.960.29-60.jb.1.11 | $60$ | $2$ | $2$ | $29$ | $11$ | $1^{14}$ |
60.960.29-60.nb.1.11 | $60$ | $2$ | $2$ | $29$ | $5$ | $1^{14}$ |
60.960.29-60.ni.1.11 | $60$ | $2$ | $2$ | $29$ | $6$ | $1^{14}$ |
60.960.33-60.cp.1.3 | $60$ | $2$ | $2$ | $33$ | $10$ | $1^{18}$ |
60.960.33-60.cr.1.4 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.ig.1.3 | $60$ | $2$ | $2$ | $33$ | $13$ | $1^{18}$ |
60.960.33-60.ij.1.4 | $60$ | $2$ | $2$ | $33$ | $8$ | $1^{18}$ |
60.960.33-60.mc.1.8 | $60$ | $2$ | $2$ | $33$ | $15$ | $1^{18}$ |
60.960.33-60.mf.1.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.mk.1.8 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
60.960.33-60.mn.1.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.rp.1.12 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{18}$ |
60.960.33-60.rs.1.11 | $60$ | $2$ | $2$ | $33$ | $12$ | $1^{18}$ |
60.960.33-60.rx.1.12 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
60.960.33-60.sa.1.11 | $60$ | $2$ | $2$ | $33$ | $4$ | $1^{18}$ |
60.960.33-60.sn.1.15 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.sq.1.16 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{18}$ |
60.960.33-60.sw.1.15 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{18}$ |
60.960.33-60.sy.1.24 | $60$ | $2$ | $2$ | $33$ | $11$ | $1^{18}$ |
60.1440.43-30.s.1.6 | $60$ | $3$ | $3$ | $43$ | $6$ | $1^{28}$ |
60.1440.49-30.de.1.5 | $60$ | $3$ | $3$ | $49$ | $9$ | $1^{32}\cdot2$ |