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Properties

Label 280.144.7.he.1
Level $280$
Index $144$
Genus $7$
Cusps $12$
$\Q$-cusps $4$

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Invariants

Level: $280$ $\SL_2$-level: $40$ Newform level: $1$
Index: $144$ $\PSL_2$-index:$144$
Genus: $7 = 1 + \frac{ 144 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$
Cusps: $12$ (of which $4$ are rational) Cusp widths $2^{4}\cdot8^{2}\cdot10^{4}\cdot40^{2}$ Cusp orbits $1^{4}\cdot2^{4}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: not computed
$\Q$-gonality: $4 \le \gamma \le 7$
$\overline{\Q}$-gonality: $4 \le \gamma \le 7$
Rational cusps: $4$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 40M7

Level structure

$\GL_2(\Z/280\Z)$-generators: $\begin{bmatrix}9&40\\237&203\end{bmatrix}$, $\begin{bmatrix}83&240\\243&41\end{bmatrix}$, $\begin{bmatrix}131&240\\245&237\end{bmatrix}$, $\begin{bmatrix}153&260\\25&173\end{bmatrix}$, $\begin{bmatrix}197&160\\66&73\end{bmatrix}$, $\begin{bmatrix}201&20\\101&57\end{bmatrix}$, $\begin{bmatrix}233&260\\183&113\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 280.288.7-280.he.1.1, 280.288.7-280.he.1.2, 280.288.7-280.he.1.3, 280.288.7-280.he.1.4, 280.288.7-280.he.1.5, 280.288.7-280.he.1.6, 280.288.7-280.he.1.7, 280.288.7-280.he.1.8, 280.288.7-280.he.1.9, 280.288.7-280.he.1.10, 280.288.7-280.he.1.11, 280.288.7-280.he.1.12, 280.288.7-280.he.1.13, 280.288.7-280.he.1.14, 280.288.7-280.he.1.15, 280.288.7-280.he.1.16, 280.288.7-280.he.1.17, 280.288.7-280.he.1.18, 280.288.7-280.he.1.19, 280.288.7-280.he.1.20, 280.288.7-280.he.1.21, 280.288.7-280.he.1.22, 280.288.7-280.he.1.23, 280.288.7-280.he.1.24, 280.288.7-280.he.1.25, 280.288.7-280.he.1.26, 280.288.7-280.he.1.27, 280.288.7-280.he.1.28, 280.288.7-280.he.1.29, 280.288.7-280.he.1.30, 280.288.7-280.he.1.31, 280.288.7-280.he.1.32, 280.288.7-280.he.1.33, 280.288.7-280.he.1.34, 280.288.7-280.he.1.35, 280.288.7-280.he.1.36, 280.288.7-280.he.1.37, 280.288.7-280.he.1.38, 280.288.7-280.he.1.39, 280.288.7-280.he.1.40, 280.288.7-280.he.1.41, 280.288.7-280.he.1.42, 280.288.7-280.he.1.43, 280.288.7-280.he.1.44, 280.288.7-280.he.1.45, 280.288.7-280.he.1.46, 280.288.7-280.he.1.47, 280.288.7-280.he.1.48
Cyclic 280-isogeny field degree: $8$
Cyclic 280-torsion field degree: $768$
Full 280-torsion field degree: $10321920$

Rational points

This modular curve has 4 rational cusps but no known non-cuspidal rational points.

Modular covers

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

Factor curve Level Index Degree Genus Rank
$X_0(5)$ $5$ $24$ $24$ $0$ $0$
56.24.0.bh.1 $56$ $6$ $6$ $0$ $0$

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank
$X_0(40)$ $40$ $2$ $2$ $3$ $0$
56.24.0.bh.1 $56$ $6$ $6$ $0$ $0$
280.72.3.bq.1 $280$ $2$ $2$ $3$ $?$
280.72.3.ct.1 $280$ $2$ $2$ $3$ $?$

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

Covering curve Level Index Degree Genus
280.288.13.cgn.1 $280$ $2$ $2$ $13$
280.288.13.cgn.2 $280$ $2$ $2$ $13$
280.288.13.cgr.1 $280$ $2$ $2$ $13$
280.288.13.cgr.2 $280$ $2$ $2$ $13$
280.288.13.chd.1 $280$ $2$ $2$ $13$
280.288.13.chd.2 $280$ $2$ $2$ $13$
280.288.13.chh.1 $280$ $2$ $2$ $13$
280.288.13.chh.2 $280$ $2$ $2$ $13$
280.288.13.cxt.1 $280$ $2$ $2$ $13$
280.288.13.cxt.2 $280$ $2$ $2$ $13$
280.288.13.cxx.1 $280$ $2$ $2$ $13$
280.288.13.cxx.2 $280$ $2$ $2$ $13$
280.288.13.cyj.1 $280$ $2$ $2$ $13$
280.288.13.cyj.2 $280$ $2$ $2$ $13$
280.288.13.cyn.1 $280$ $2$ $2$ $13$
280.288.13.cyn.2 $280$ $2$ $2$ $13$
280.288.15.lo.1 $280$ $2$ $2$ $15$
280.288.15.lo.2 $280$ $2$ $2$ $15$
280.288.15.lp.1 $280$ $2$ $2$ $15$
280.288.15.lp.2 $280$ $2$ $2$ $15$
280.288.15.lq.1 $280$ $2$ $2$ $15$
280.288.15.lq.2 $280$ $2$ $2$ $15$
280.288.15.lq.3 $280$ $2$ $2$ $15$
280.288.15.lq.4 $280$ $2$ $2$ $15$
280.288.15.lr.1 $280$ $2$ $2$ $15$
280.288.15.lr.2 $280$ $2$ $2$ $15$
280.288.15.lr.3 $280$ $2$ $2$ $15$
280.288.15.lr.4 $280$ $2$ $2$ $15$
280.288.15.ls.1 $280$ $2$ $2$ $15$
280.288.15.ls.2 $280$ $2$ $2$ $15$
280.288.15.lt.1 $280$ $2$ $2$ $15$
280.288.15.lt.2 $280$ $2$ $2$ $15$