Invariants
| Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $1200$ | ||
| Index: | $1920$ | $\PSL_2$-index: | $960$ | ||||
| Genus: | $69 = 1 + \frac{ 960 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $20^{12}\cdot60^{12}$ | Cusp orbits | $2^{2}\cdot4^{5}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $6$ | ||||||
| $\Q$-gonality: | $10 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $10 \le \gamma \le 20$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.1920.69.6438 |
Level structure
| $\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}1&20\\18&59\end{bmatrix}$, $\begin{bmatrix}35&42\\42&11\end{bmatrix}$, $\begin{bmatrix}37&8\\18&11\end{bmatrix}$, $\begin{bmatrix}49&40\\42&1\end{bmatrix}$, $\begin{bmatrix}55&24\\24&47\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 60.960.69.cq.1 for the level structure with $-I$) |
| Cyclic 60-isogeny field degree: | $12$ |
| Cyclic 60-torsion field degree: | $96$ |
| Full 60-torsion field degree: | $1152$ |
Jacobian
| Conductor: | $2^{196}\cdot3^{55}\cdot5^{138}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{33}\cdot2^{4}\cdot4^{3}\cdot8^{2}$ |
| Newforms: | 50.2.a.b$^{4}$, 75.2.a.a$^{3}$, 75.2.a.b$^{3}$, 100.2.a.a$^{2}$, 150.2.a.b$^{2}$, 300.2.a.b, 300.2.e.c, 300.2.e.e, 400.2.a.a$^{2}$, 400.2.a.b$^{2}$, 400.2.a.f$^{2}$, 400.2.a.g$^{2}$, 1200.2.a.a, 1200.2.a.c, 1200.2.a.g, 1200.2.a.h, 1200.2.a.j, 1200.2.a.l, 1200.2.a.m, 1200.2.a.n, 1200.2.a.q, 1200.2.a.s, 1200.2.h.a, 1200.2.h.c, 1200.2.h.f, 1200.2.h.i, 1200.2.h.j, 1200.2.h.l, 1200.2.h.n |
Rational points
This modular curve has no $\Q_p$ points for $p=7,13,43,53$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.960.31-60.a.2.7 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot2^{4}\cdot4^{3}$ |
| 60.960.31-60.a.2.35 | $60$ | $2$ | $2$ | $31$ | $0$ | $1^{18}\cdot2^{4}\cdot4^{3}$ |
| 60.960.33-60.x.1.16 | $60$ | $2$ | $2$ | $33$ | $6$ | $2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.960.33-60.x.1.25 | $60$ | $2$ | $2$ | $33$ | $6$ | $2^{4}\cdot4^{3}\cdot8^{2}$ |
| 60.960.35-60.q.2.4 | $60$ | $2$ | $2$ | $35$ | $0$ | $1^{18}\cdot8^{2}$ |
| 60.960.35-60.q.2.21 | $60$ | $2$ | $2$ | $35$ | $0$ | $1^{18}\cdot8^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 60.3840.137-60.cw.1.2 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cw.1.15 | $60$ | $2$ | $2$ | $137$ | $19$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cx.1.16 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cx.4.4 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cz.1.14 | $60$ | $2$ | $2$ | $137$ | $24$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.cz.4.7 | $60$ | $2$ | $2$ | $137$ | $24$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.db.2.13 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.db.4.7 | $60$ | $2$ | $2$ | $137$ | $18$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ix.1.13 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ix.4.7 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.iy.1.2 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.iy.2.13 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.jb.2.2 | $60$ | $2$ | $2$ | $137$ | $22$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.jb.3.15 | $60$ | $2$ | $2$ | $137$ | $22$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.jc.1.15 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.jc.4.2 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{36}\cdot4^{2}\cdot8^{3}$ |
| 60.3840.137-60.ki.1.6 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.kl.2.7 | $60$ | $2$ | $2$ | $137$ | $15$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.ku.2.3 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.kx.1.7 | $60$ | $2$ | $2$ | $137$ | $11$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.nk.1.5 | $60$ | $2$ | $2$ | $137$ | $14$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.nn.1.2 | $60$ | $2$ | $2$ | $137$ | $12$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.nw.1.6 | $60$ | $2$ | $2$ | $137$ | $17$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.3840.137-60.nz.2.1 | $60$ | $2$ | $2$ | $137$ | $20$ | $1^{32}\cdot2^{6}\cdot4^{4}\cdot8$ |
| 60.5760.205-60.hx.1.28 | $60$ | $3$ | $3$ | $205$ | $18$ | $1^{64}\cdot2^{6}\cdot4^{9}\cdot8^{3}$ |
| 60.5760.217-60.pt.1.13 | $60$ | $3$ | $3$ | $217$ | $29$ | $1^{70}\cdot2^{9}\cdot4^{7}\cdot8^{4}$ |