Invariants
Level: | $60$ | $\SL_2$-level: | $20$ | Newform level: | $3600$ | ||
Index: | $240$ | $\PSL_2$-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 | $20^{12}$ | Cusp orbits | $4^{3}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | $6$ | ||||||
$\Q$-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: | 20D15 |
Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 60.240.15.166 |
Level structure
$\GL_2(\Z/60\Z)$-generators: | $\begin{bmatrix}9&32\\29&31\end{bmatrix}$, $\begin{bmatrix}27&58\\26&33\end{bmatrix}$, $\begin{bmatrix}37&46\\57&23\end{bmatrix}$, $\begin{bmatrix}59&32\\39&13\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 60-isogeny field degree: | $48$ |
Cyclic 60-torsion field degree: | $768$ |
Full 60-torsion field degree: | $9216$ |
Jacobian
Conductor: | $2^{38}\cdot3^{16}\cdot5^{26}$ |
Simple: | no |
Squarefree: | yes |
Decomposition: | $1^{15}$ |
Newforms: | 20.2.a.a, 40.2.a.a, 50.2.a.a, 50.2.a.b, 180.2.a.a, 200.2.a.a, 360.2.a.a, 400.2.a.a, 400.2.a.e, 450.2.a.c, 450.2.a.g, 900.2.a.b, 1800.2.a.r, 3600.2.a.bc, 3600.2.a.be |
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 |
---|---|---|---|---|---|---|
20.120.7.ct.1 | $20$ | $2$ | $2$ | $7$ | $2$ | $1^{8}$ |
60.24.0.l.1 | $60$ | $10$ | $10$ | $0$ | $0$ | full Jacobian |
60.120.7.dl.1 | $60$ | $2$ | $2$ | $7$ | $5$ | $1^{8}$ |
60.120.7.jx.1 | $60$ | $2$ | $2$ | $7$ | $3$ | $1^{8}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
60.480.29.im.1 | $60$ | $2$ | $2$ | $29$ | $8$ | $1^{14}$ |
60.480.29.iq.1 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.480.29.jj.1 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
60.480.29.jn.1 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.480.29.kn.1 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.480.29.kr.1 | $60$ | $2$ | $2$ | $29$ | $10$ | $1^{14}$ |
60.480.29.ln.1 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.480.29.lr.1 | $60$ | $2$ | $2$ | $29$ | $12$ | $1^{14}$ |
60.720.43.kf.1 | $60$ | $3$ | $3$ | $43$ | $15$ | $1^{28}$ |
60.720.55.xo.1 | $60$ | $3$ | $3$ | $55$ | $19$ | $1^{40}$ |
60.960.69.ng.1 | $60$ | $4$ | $4$ | $69$ | $22$ | $1^{54}$ |