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Properties

Label 120.48.1.zf.1
Level $120$
Index $48$
Genus $1$
Cusps $8$
$\Q$-cusps $4$

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Invariants

Level: $120$ $\SL_2$-level: $12$ Newform level: $1$
Index: $48$ $\PSL_2$-index:$48$
Genus: $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$
Cusps: $8$ (of which $4$ are rational) Cusp widths $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ Cusp orbits $1^{4}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2$
$\overline{\Q}$-gonality: $2$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 12P1

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}11&21\\116&115\end{bmatrix}$, $\begin{bmatrix}17&40\\0&19\end{bmatrix}$, $\begin{bmatrix}21&65\\92&33\end{bmatrix}$, $\begin{bmatrix}41&10\\20&39\end{bmatrix}$, $\begin{bmatrix}49&39\\40&113\end{bmatrix}$, $\begin{bmatrix}93&94\\4&33\end{bmatrix}$, $\begin{bmatrix}119&58\\72&37\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.96.1-120.zf.1.1, 120.96.1-120.zf.1.2, 120.96.1-120.zf.1.3, 120.96.1-120.zf.1.4, 120.96.1-120.zf.1.5, 120.96.1-120.zf.1.6, 120.96.1-120.zf.1.7, 120.96.1-120.zf.1.8, 120.96.1-120.zf.1.9, 120.96.1-120.zf.1.10, 120.96.1-120.zf.1.11, 120.96.1-120.zf.1.12, 120.96.1-120.zf.1.13, 120.96.1-120.zf.1.14, 120.96.1-120.zf.1.15, 120.96.1-120.zf.1.16, 120.96.1-120.zf.1.17, 120.96.1-120.zf.1.18, 120.96.1-120.zf.1.19, 120.96.1-120.zf.1.20, 120.96.1-120.zf.1.21, 120.96.1-120.zf.1.22, 120.96.1-120.zf.1.23, 120.96.1-120.zf.1.24, 120.96.1-120.zf.1.25, 120.96.1-120.zf.1.26, 120.96.1-120.zf.1.27, 120.96.1-120.zf.1.28, 120.96.1-120.zf.1.29, 120.96.1-120.zf.1.30, 120.96.1-120.zf.1.31, 120.96.1-120.zf.1.32, 120.96.1-120.zf.1.33, 120.96.1-120.zf.1.34, 120.96.1-120.zf.1.35, 120.96.1-120.zf.1.36, 120.96.1-120.zf.1.37, 120.96.1-120.zf.1.38, 120.96.1-120.zf.1.39, 120.96.1-120.zf.1.40
Cyclic 120-isogeny field degree: $12$
Cyclic 120-torsion field degree: $384$
Full 120-torsion field degree: $737280$

Jacobian

Conductor: $?$
Simple: yes
Squarefree: yes
Decomposition: $1$
Newforms: not computed

Rational points

This modular curve is an elliptic curve, but the rank has not been computed

Modular covers

The following modular covers realize this modular curve as a fiber product over $X(1)$.

Factor curve Level Index Degree Genus Rank Kernel decomposition
$X_0(3)$ $3$ $12$ $12$ $0$ $0$ full Jacobian
40.12.0.v.1 $40$ $4$ $4$ $0$ $0$ full Jacobian

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
$X_0(12)$ $12$ $2$ $2$ $0$ $0$ full Jacobian
40.12.0.v.1 $40$ $4$ $4$ $0$ $0$ full Jacobian
120.24.0.fn.1 $120$ $2$ $2$ $0$ $?$ full Jacobian
120.24.1.ix.1 $120$ $2$ $2$ $1$ $?$ 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
120.96.1.rv.1 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rv.2 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rv.3 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rv.4 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rw.1 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rw.2 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rw.3 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.1.rw.4 $120$ $2$ $2$ $1$ $?$ dimension zero
120.96.3.nf.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.nf.2 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.nh.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.nh.2 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.oe.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.of.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.oq.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.or.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.pc.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.pd.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.pg.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.ph.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.rb.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.rb.2 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.rd.1 $120$ $2$ $2$ $3$ $?$ not computed
120.96.3.rd.2 $120$ $2$ $2$ $3$ $?$ not computed
120.144.5.bbf.1 $120$ $3$ $3$ $5$ $?$ not computed
120.240.17.bql.1 $120$ $5$ $5$ $17$ $?$ not computed
120.288.17.bkfp.1 $120$ $6$ $6$ $17$ $?$ not computed