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Properties

Label 120.96.3.ib.1
Level $120$
Index $96$
Genus $3$
Cusps $12$
$\Q$-cusps $0$

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Invariants

Level: $120$ $\SL_2$-level: $12$ Newform level: $1$
Index: $96$ $\PSL_2$-index:$96$
Genus: $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (none of which are rational) Cusp widths $4^{6}\cdot12^{6}$ Cusp orbits $2^{2}\cdot4^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $2 \le \gamma \le 4$
$\overline{\Q}$-gonality: $2 \le \gamma \le 3$
Rational cusps: $0$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 12K3

Level structure

$\GL_2(\Z/120\Z)$-generators: $\begin{bmatrix}12&13\\13&96\end{bmatrix}$, $\begin{bmatrix}36&71\\5&108\end{bmatrix}$, $\begin{bmatrix}51&62\\38&87\end{bmatrix}$, $\begin{bmatrix}77&36\\16&109\end{bmatrix}$, $\begin{bmatrix}103&16\\20&87\end{bmatrix}$, $\begin{bmatrix}109&28\\12&47\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 120.192.3-120.ib.1.1, 120.192.3-120.ib.1.2, 120.192.3-120.ib.1.3, 120.192.3-120.ib.1.4, 120.192.3-120.ib.1.5, 120.192.3-120.ib.1.6, 120.192.3-120.ib.1.7, 120.192.3-120.ib.1.8, 120.192.3-120.ib.1.9, 120.192.3-120.ib.1.10, 120.192.3-120.ib.1.11, 120.192.3-120.ib.1.12, 120.192.3-120.ib.1.13, 120.192.3-120.ib.1.14, 120.192.3-120.ib.1.15, 120.192.3-120.ib.1.16, 120.192.3-120.ib.1.17, 120.192.3-120.ib.1.18, 120.192.3-120.ib.1.19, 120.192.3-120.ib.1.20, 120.192.3-120.ib.1.21, 120.192.3-120.ib.1.22, 120.192.3-120.ib.1.23, 120.192.3-120.ib.1.24, 120.192.3-120.ib.1.25, 120.192.3-120.ib.1.26, 120.192.3-120.ib.1.27, 120.192.3-120.ib.1.28, 120.192.3-120.ib.1.29, 120.192.3-120.ib.1.30, 120.192.3-120.ib.1.31, 120.192.3-120.ib.1.32
Cyclic 120-isogeny field degree: $24$
Cyclic 120-torsion field degree: $768$
Full 120-torsion field degree: $368640$

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
24.48.1.cu.1 $24$ $2$ $2$ $1$ $0$
60.48.2.f.1 $60$ $2$ $2$ $2$ $1$
120.24.0.bd.1 $120$ $4$ $4$ $0$ $?$
120.48.2.q.1 $120$ $2$ $2$ $2$ $?$

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

Covering curve Level Index Degree Genus
120.192.9.st.1 $120$ $2$ $2$ $9$
120.192.9.sv.1 $120$ $2$ $2$ $9$
120.192.9.sz.1 $120$ $2$ $2$ $9$
120.192.9.tf.1 $120$ $2$ $2$ $9$
120.192.9.tj.1 $120$ $2$ $2$ $9$
120.192.9.tt.1 $120$ $2$ $2$ $9$
120.192.9.tx.1 $120$ $2$ $2$ $9$
120.192.9.ul.1 $120$ $2$ $2$ $9$
120.192.9.un.1 $120$ $2$ $2$ $9$
120.192.9.vb.1 $120$ $2$ $2$ $9$
120.192.9.vf.1 $120$ $2$ $2$ $9$
120.192.9.vp.1 $120$ $2$ $2$ $9$
120.192.9.vt.1 $120$ $2$ $2$ $9$
120.192.9.vz.1 $120$ $2$ $2$ $9$
120.192.9.wf.1 $120$ $2$ $2$ $9$
120.192.9.wh.1 $120$ $2$ $2$ $9$
120.288.13.bri.1 $120$ $3$ $3$ $13$