Invariants
Level: | $60$ | $\SL_2$-level: | $60$ | Newform level: | $720$ | ||
Index: | $576$ | $\PSL_2$-index: | $288$ | ||||
Genus: | $13 = 1 + \frac{ 288 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
Cusps: | $24$ (none of which are rational) | Cusp widths | $1^{4}\cdot3^{4}\cdot4^{2}\cdot5^{4}\cdot12^{2}\cdot15^{4}\cdot20^{2}\cdot60^{2}$ | Cusp orbits | $2^{8}\cdot4^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $1$ | ||||||
$\Q$-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: | 60AJ13 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.576.13.6390 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}23&15\\32&59\end{bmatrix}$, $\begin{bmatrix}29&15\\36&41\end{bmatrix}$, $\begin{bmatrix}41&30\\8&31\end{bmatrix}$, $\begin{bmatrix}59&45\\14&13\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 60.288.13.mi.2 for the level structure with $-I$) |
Cyclic 60-isogeny field degree: | $2$ |
Cyclic 60-torsion field degree: | $16$ |
Full 60-torsion field degree: | $3840$ |
Jacobian
Conductor: | $2^{31}\cdot3^{19}\cdot5^{13}$ |
Simple: | no |
Squarefree: | no |
Decomposition: | $1^{7}\cdot2^{3}$ |
Newforms: | 15.2.a.a$^{2}$, 30.2.a.a, 30.2.c.a, 60.2.d.a, 720.2.a.c, 720.2.a.h$^{2}$, 720.2.a.j, 720.2.f.f |
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 |
---|---|---|---|---|---|---|
60.288.5-60.od.2.11 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}\cdot2^{2}$ |
60.288.5-60.od.2.29 | $60$ | $2$ | $2$ | $5$ | $0$ | $1^{4}\cdot2^{2}$ |
60.288.7-60.jz.1.4 | $60$ | $2$ | $2$ | $7$ | $1$ | $2^{3}$ |
60.288.7-60.jz.1.25 | $60$ | $2$ | $2$ | $7$ | $1$ | $2^{3}$ |
60.288.7-60.me.1.6 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2$ |
60.288.7-60.me.1.16 | $60$ | $2$ | $2$ | $7$ | $0$ | $1^{4}\cdot2$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
60.1152.33-60.ba.1.16 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.cr.1.12 | $60$ | $2$ | $2$ | $33$ | $3$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.ie.2.5 | $60$ | $2$ | $2$ | $33$ | $1$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.ig.2.7 | $60$ | $2$ | $2$ | $33$ | $5$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.lc.2.7 | $60$ | $2$ | $2$ | $33$ | $6$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.ld.2.5 | $60$ | $2$ | $2$ | $33$ | $7$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.lm.1.12 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{10}\cdot2^{5}$ |
60.1152.33-60.ln.1.9 | $60$ | $2$ | $2$ | $33$ | $2$ | $1^{10}\cdot2^{5}$ |
60.1728.49-60.gc.2.5 | $60$ | $3$ | $3$ | $49$ | $3$ | $1^{18}\cdot2^{9}$ |
60.2880.85-60.kn.1.2 | $60$ | $5$ | $5$ | $85$ | $10$ | $1^{36}\cdot2^{18}$ |