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Properties

Label 60.96.1.f.4
Level $60$
Index $96$
Genus $1$
Analytic rank $0$
Cusps $16$
$\Q$-cusps $2$

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Invariants

Level: $60$ $\SL_2$-level: $12$ Newform level: $600$
Index: $96$ $\PSL_2$-index:$96$
Genus: $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$
Cusps: $16$ (of which $2$ are rational) Cusp widths $2^{4}\cdot4^{4}\cdot6^{4}\cdot12^{4}$ Cusp orbits $1^{2}\cdot2^{3}\cdot4^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $0$
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 12V1
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 60.96.1.63

Level structure

$\GL_2(\Z/60\Z)$-generators: $\begin{bmatrix}7&58\\54&17\end{bmatrix}$, $\begin{bmatrix}11&14\\24&5\end{bmatrix}$, $\begin{bmatrix}13&2\\54&55\end{bmatrix}$, $\begin{bmatrix}19&52\\42&59\end{bmatrix}$, $\begin{bmatrix}29&2\\24&13\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 60.192.1-60.f.4.1, 60.192.1-60.f.4.2, 60.192.1-60.f.4.3, 60.192.1-60.f.4.4, 60.192.1-60.f.4.5, 60.192.1-60.f.4.6, 60.192.1-60.f.4.7, 60.192.1-60.f.4.8, 60.192.1-60.f.4.9, 60.192.1-60.f.4.10, 60.192.1-60.f.4.11, 60.192.1-60.f.4.12, 60.192.1-60.f.4.13, 60.192.1-60.f.4.14, 60.192.1-60.f.4.15, 60.192.1-60.f.4.16, 120.192.1-60.f.4.1, 120.192.1-60.f.4.2, 120.192.1-60.f.4.3, 120.192.1-60.f.4.4, 120.192.1-60.f.4.5, 120.192.1-60.f.4.6, 120.192.1-60.f.4.7, 120.192.1-60.f.4.8, 120.192.1-60.f.4.9, 120.192.1-60.f.4.10, 120.192.1-60.f.4.11, 120.192.1-60.f.4.12, 120.192.1-60.f.4.13, 120.192.1-60.f.4.14, 120.192.1-60.f.4.15, 120.192.1-60.f.4.16
Cyclic 60-isogeny field degree: $12$
Cyclic 60-torsion field degree: $192$
Full 60-torsion field degree: $23040$

Jacobian

Conductor: $2^{3}\cdot3\cdot5^{2}$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: 600.2.a.h

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

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Cover information

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This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
12.48.0.a.2 $12$ $2$ $2$ $0$ $0$ full Jacobian
60.48.0.a.1 $60$ $2$ $2$ $0$ $0$ full Jacobian
60.48.1.b.1 $60$ $2$ $2$ $1$ $0$ dimension zero

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
60.192.5.g.1 $60$ $2$ $2$ $5$ $0$ $1^{2}\cdot2$
60.192.5.h.2 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.m.2 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.o.2 $60$ $2$ $2$ $5$ $0$ $1^{2}\cdot2$
60.192.5.q.2 $60$ $2$ $2$ $5$ $0$ $1^{2}\cdot2$
60.192.5.r.3 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.w.3 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.y.2 $60$ $2$ $2$ $5$ $0$ $1^{2}\cdot2$
60.288.9.d.2 $60$ $3$ $3$ $9$ $1$ $1^{4}\cdot2^{2}$
60.480.33.j.3 $60$ $5$ $5$ $33$ $1$ $1^{16}\cdot8^{2}$
60.576.33.j.4 $60$ $6$ $6$ $33$ $1$ $1^{16}\cdot8^{2}$
60.960.65.j.1 $60$ $10$ $10$ $65$ $1$ $1^{32}\cdot8^{4}$
120.192.5.iu.3 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.ja.2 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.ke.3 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.ks.2 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.og.2 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.om.3 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.pq.2 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.qe.3 $120$ $2$ $2$ $5$ $?$ not computed
180.288.9.f.4 $180$ $3$ $3$ $9$ $?$ not computed
180.288.17.f.3 $180$ $3$ $3$ $17$ $?$ not computed
180.288.17.n.4 $180$ $3$ $3$ $17$ $?$ not computed