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Properties

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

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Invariants

Level: $60$ $\SL_2$-level: $12$ Newform level: $1800$
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: $1$
$\Q$-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: 60.96.1.57

Level structure

$\GL_2(\Z/60\Z)$-generators: $\begin{bmatrix}13&20\\36&7\end{bmatrix}$, $\begin{bmatrix}19&24\\30&29\end{bmatrix}$, $\begin{bmatrix}35&52\\6&53\end{bmatrix}$, $\begin{bmatrix}49&16\\6&31\end{bmatrix}$, $\begin{bmatrix}49&50\\18&7\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 60.192.1-60.h.4.1, 60.192.1-60.h.4.2, 60.192.1-60.h.4.3, 60.192.1-60.h.4.4, 60.192.1-60.h.4.5, 60.192.1-60.h.4.6, 60.192.1-60.h.4.7, 60.192.1-60.h.4.8, 60.192.1-60.h.4.9, 60.192.1-60.h.4.10, 60.192.1-60.h.4.11, 60.192.1-60.h.4.12, 60.192.1-60.h.4.13, 60.192.1-60.h.4.14, 60.192.1-60.h.4.15, 60.192.1-60.h.4.16, 120.192.1-60.h.4.1, 120.192.1-60.h.4.2, 120.192.1-60.h.4.3, 120.192.1-60.h.4.4, 120.192.1-60.h.4.5, 120.192.1-60.h.4.6, 120.192.1-60.h.4.7, 120.192.1-60.h.4.8, 120.192.1-60.h.4.9, 120.192.1-60.h.4.10, 120.192.1-60.h.4.11, 120.192.1-60.h.4.12, 120.192.1-60.h.4.13, 120.192.1-60.h.4.14, 120.192.1-60.h.4.15, 120.192.1-60.h.4.16
Cyclic 60-isogeny field degree: $12$
Cyclic 60-torsion field degree: $192$
Full 60-torsion field degree: $23040$

Jacobian

Conductor: $2^{3}\cdot3^{2}\cdot5^{2}$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: 1800.2.a.m

Rational points

This modular curve has infinitely many rational points, including 1 stored non-cuspidal point.

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.2 $60$ $2$ $2$ $0$ $0$ full Jacobian
60.48.1.d.1 $60$ $2$ $2$ $1$ $1$ 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.j.2 $60$ $2$ $2$ $5$ $2$ $1^{2}\cdot2$
60.192.5.k.3 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.m.1 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.n.1 $60$ $2$ $2$ $5$ $2$ $1^{2}\cdot2$
60.192.5.t.2 $60$ $2$ $2$ $5$ $2$ $1^{2}\cdot2$
60.192.5.u.4 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.w.1 $60$ $2$ $2$ $5$ $1$ $1^{2}\cdot2$
60.192.5.x.1 $60$ $2$ $2$ $5$ $2$ $1^{2}\cdot2$
60.288.9.e.2 $60$ $3$ $3$ $9$ $2$ $1^{4}\cdot2^{2}$
60.480.33.l.1 $60$ $5$ $5$ $33$ $3$ $1^{16}\cdot8^{2}$
60.576.33.l.3 $60$ $6$ $6$ $33$ $5$ $1^{16}\cdot8^{2}$
60.960.65.l.2 $60$ $10$ $10$ $65$ $5$ $1^{32}\cdot8^{4}$
120.192.5.jl.4 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.jr.3 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.kf.1 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.km.1 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.ox.3 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.pd.4 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.pr.1 $120$ $2$ $2$ $5$ $?$ not computed
120.192.5.py.1 $120$ $2$ $2$ $5$ $?$ not computed
180.288.9.h.2 $180$ $3$ $3$ $9$ $?$ not computed
180.288.17.h.1 $180$ $3$ $3$ $17$ $?$ not computed
180.288.17.p.2 $180$ $3$ $3$ $17$ $?$ not computed