Invariants
Level: | $84$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $36$ | $\PSL_2$-index: | $36$ | ||||
Genus: | $1 = 1 + \frac{ 36 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$ | ||||||
Cusps: | $6$ (of which $2$ are rational) | Cusp widths | $3^{4}\cdot12^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}$ | ||
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: | 12K1 |
Level structure
$\GL_2(\Z/84\Z)$-generators: | $\begin{bmatrix}4&51\\33&4\end{bmatrix}$, $\begin{bmatrix}22&45\\33&34\end{bmatrix}$, $\begin{bmatrix}24&31\\43&48\end{bmatrix}$, $\begin{bmatrix}75&46\\26&45\end{bmatrix}$, $\begin{bmatrix}79&18\\60&23\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 84-isogeny field degree: | $32$ |
Cyclic 84-torsion field degree: | $768$ |
Full 84-torsion field degree: | $258048$ |
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 |
---|---|---|---|---|---|---|
6.18.0.b.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.18.0.g.1 | $84$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
84.18.1.e.1 | $84$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
84.72.1.r.1 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.72.1.s.1 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.72.1.bm.1 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.72.1.bn.1 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.72.3.bc.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.cn.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.lx.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.ly.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.nb.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.nc.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.ox.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.oy.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.qz.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.ra.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.ri.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.72.3.rk.1 | $84$ | $2$ | $2$ | $3$ | $?$ | not computed |
84.288.19.gi.1 | $84$ | $8$ | $8$ | $19$ | $?$ | not computed |
168.72.1.ce.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.72.1.ch.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.72.1.ey.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.72.1.fb.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.72.3.hw.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.re.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.dii.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.dil.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.dno.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.dnv.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.eam.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.eat.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.emi.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.eml.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.ens.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.72.3.eog.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
252.108.4.f.1 | $252$ | $3$ | $3$ | $4$ | $?$ | not computed |
252.108.7.gg.1 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |