Invariants
Level: | $126$ | $\SL_2$-level: | $18$ | Newform level: | $1$ | ||
Index: | $216$ | $\PSL_2$-index: | $108$ | ||||
Genus: | $2 = 1 + \frac{ 108 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $3^{6}\cdot6^{6}\cdot9^{2}\cdot18^{2}$ | Cusp orbits | $2^{2}\cdot3^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 18P2 |
Level structure
$\GL_2(\Z/126\Z)$-generators: | $\begin{bmatrix}61&111\\54&37\end{bmatrix}$, $\begin{bmatrix}101&39\\30&65\end{bmatrix}$, $\begin{bmatrix}125&102\\24&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 126.108.2.a.1 for the level structure with $-I$) |
Cyclic 126-isogeny field degree: | $24$ |
Cyclic 126-torsion field degree: | $864$ |
Full 126-torsion field degree: | $217728$ |
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
$X_0(2)$ | $2$ | $72$ | $36$ | $0$ | $0$ |
63.72.0-63.a.1.2 | $63$ | $3$ | $3$ | $0$ | $0$ |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
42.72.0-6.a.1.1 | $42$ | $3$ | $3$ | $0$ | $0$ |
63.72.0-63.a.1.2 | $63$ | $3$ | $3$ | $0$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
126.432.7-126.a.1.3 | $126$ | $2$ | $2$ | $7$ |
126.432.7-126.ch.1.3 | $126$ | $2$ | $2$ | $7$ |
126.432.7-126.cj.1.2 | $126$ | $2$ | $2$ | $7$ |
126.432.7-126.cl.1.2 | $126$ | $2$ | $2$ | $7$ |
252.432.7-252.c.1.17 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.m.1.3 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.n.1.5 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.cg.1.9 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.ch.1.1 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.ci.1.3 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.cq.1.1 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.cr.1.2 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.cs.1.5 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.da.1.2 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.db.1.1 | $252$ | $2$ | $2$ | $7$ |
252.432.7-252.dc.1.5 | $252$ | $2$ | $2$ | $7$ |
252.432.11-252.bi.1.3 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.bj.1.1 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.bu.1.1 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.bv.1.3 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.cm.1.1 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.cn.1.2 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.de.1.2 | $252$ | $2$ | $2$ | $11$ |
252.432.11-252.df.1.1 | $252$ | $2$ | $2$ | $11$ |