Invariants
Level: | $84$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2\cdot4\cdot6\cdot12$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12F1 |
Level structure
$\GL_2(\Z/84\Z)$-generators: | $\begin{bmatrix}16&71\\43&78\end{bmatrix}$, $\begin{bmatrix}26&49\\69&82\end{bmatrix}$, $\begin{bmatrix}28&57\\31&38\end{bmatrix}$, $\begin{bmatrix}81&52\\2&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.24.1.m.1 for the level structure with $-I$) |
Cyclic 84-isogeny field degree: | $16$ |
Cyclic 84-torsion field degree: | $192$ |
Full 84-torsion field degree: | $193536$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
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 |
---|---|---|---|---|---|---|
12.24.0-6.a.1.11 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
42.24.0-6.a.1.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
84.96.1-84.d.1.19 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.f.1.10 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.n.1.3 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.o.1.8 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.r.1.4 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.s.1.3 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.v.1.6 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1-84.w.1.8 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.144.3-84.jx.1.8 | $84$ | $3$ | $3$ | $3$ | $?$ | not computed |
84.384.13-84.x.1.5 | $84$ | $8$ | $8$ | $13$ | $?$ | not computed |
168.96.1-168.gj.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.kb.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zl.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.zo.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.baf.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bai.1.5 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bar.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1-168.bau.1.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
252.144.3-252.cc.1.11 | $252$ | $3$ | $3$ | $3$ | $?$ | not computed |
252.144.5-252.n.1.4 | $252$ | $3$ | $3$ | $5$ | $?$ | not computed |
252.144.5-252.r.1.3 | $252$ | $3$ | $3$ | $5$ | $?$ | not computed |