Invariants
| Level: | $126$ | $\SL_2$-level: | $18$ | Newform level: | $1$ | ||
| Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
| Genus: | $2 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 2 }{2}$ | ||||||
| Cusps: | $2$ (all of which are rational) | Cusp widths | $6\cdot18$ | Cusp orbits | $1^{2}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | not computed | ||||||
| $\Q$-gonality: | $2$ | ||||||
| $\overline{\Q}$-gonality: | $2$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 18B2 |
Level structure
| $\GL_2(\Z/126\Z)$-generators: | $\begin{bmatrix}35&123\\29&94\end{bmatrix}$, $\begin{bmatrix}45&77\\92&75\end{bmatrix}$, $\begin{bmatrix}87&35\\7&62\end{bmatrix}$ |
| Contains $-I$: | no $\quad$ (see 126.24.2.b.1 for the level structure with $-I$) |
| Cyclic 126-isogeny field degree: | $72$ |
| Cyclic 126-torsion field degree: | $2592$ |
| Full 126-torsion field degree: | $979776$ |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank |
|---|---|---|---|---|---|
| 18.24.1-9.a.1.2 | $18$ | $2$ | $2$ | $1$ | $0$ |
| 42.16.0-42.b.1.1 | $42$ | $3$ | $3$ | $0$ | $0$ |
| 63.24.1-9.a.1.1 | $63$ | $2$ | $2$ | $1$ | $0$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus |
|---|---|---|---|---|
| 126.144.4-126.p.1.4 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.s.1.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.s.2.1 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.v.1.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.v.2.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.z.1.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.z.2.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.ba.1.1 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.bb.1.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.bb.2.2 | $126$ | $3$ | $3$ | $4$ |
| 126.144.4-126.bc.1.2 | $126$ | $3$ | $3$ | $4$ |
| 126.384.15-126.e.1.7 | $126$ | $8$ | $8$ | $15$ |
| 252.192.7-252.c.1.2 | $252$ | $4$ | $4$ | $7$ |