Invariants
Level: | $84$ | $\SL_2$-level: | $6$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $6^{12}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
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: | 6F1 |
Level structure
$\GL_2(\Z/84\Z)$-generators: | $\begin{bmatrix}0&55\\1&42\end{bmatrix}$, $\begin{bmatrix}2&21\\39&68\end{bmatrix}$, $\begin{bmatrix}35&54\\6&5\end{bmatrix}$, $\begin{bmatrix}36&49\\79&72\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.72.1.u.1 for the level structure with $-I$) |
Cyclic 84-isogeny field degree: | $16$ |
Cyclic 84-torsion field degree: | $384$ |
Full 84-torsion field degree: | $64512$ |
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 |
---|---|---|---|---|---|---|
12.72.0-6.a.1.4 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
42.72.0-6.a.1.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.48.0-84.p.1.7 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
84.48.0-84.p.1.11 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
84.48.1-84.g.1.3 | $84$ | $3$ | $3$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
84.288.5-84.ce.1.2 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.ci.1.8 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.dt.1.4 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.du.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.fp.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.fq.1.2 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.gu.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.gy.1.4 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.qm.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.ro.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdy.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bef.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bqt.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bra.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bzd.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.caf.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.432.7-252.bz.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.bz.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cg.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cg.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.di.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.di.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.dt.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ef.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ef.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.eq.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.10-252.bw.1.3 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.10-252.bw.1.5 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.13-252.cr.1.5 | $252$ | $3$ | $3$ | $13$ | $?$ | not computed |