Invariants
Level: | $168$ | $\SL_2$-level: | $8$ | Newform level: | $3136$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $2$ are rational) | Cusp widths | $4^{4}\cdot8^{4}$ | Cusp orbits | $1^{2}\cdot2^{3}$ | ||
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: | 8F1 |
Level structure
$\GL_2(\Z/168\Z)$-generators: | $\begin{bmatrix}5&72\\96&77\end{bmatrix}$, $\begin{bmatrix}31&40\\8&145\end{bmatrix}$, $\begin{bmatrix}65&156\\148&11\end{bmatrix}$, $\begin{bmatrix}79&8\\120&107\end{bmatrix}$, $\begin{bmatrix}125&16\\136&121\end{bmatrix}$, $\begin{bmatrix}159&92\\56&145\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 56.48.1.n.2 for the level structure with $-I$) |
Cyclic 168-isogeny field degree: | $64$ |
Cyclic 168-torsion field degree: | $3072$ |
Full 168-torsion field degree: | $1548288$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | 3136.2.a.m |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
12.48.0-4.b.1.1 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
168.48.0-4.b.1.5 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-56.l.1.3 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.0-56.l.1.17 | $168$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
168.48.1-56.d.1.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.48.1-56.d.1.20 | $168$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
168.192.1-56.a.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.a.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.e.1.16 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.e.2.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.g.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.g.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.r.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.r.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.w.1.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-56.w.2.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.y.1.14 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.y.2.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.bx.1.13 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.bx.2.10 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.cq.1.15 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.1-168.cq.2.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.192.3-56.j.1.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.j.2.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.l.1.3 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.l.2.3 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.o.1.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.o.2.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.q.1.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-56.q.2.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bb.1.26 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bb.2.25 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bm.2.14 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bm.3.14 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bo.1.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bo.2.32 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bu.1.30 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.192.3-168.bu.2.29 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.288.9-168.cy.1.37 | $168$ | $3$ | $3$ | $9$ | $?$ | not computed |
168.384.9-168.bo.1.49 | $168$ | $4$ | $4$ | $9$ | $?$ | not computed |