Invariants
Level: | $84$ | $\SL_2$-level: | $12$ | 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 | $3^{8}\cdot12^{4}$ | 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: | 12S1 |
Level structure
$\GL_2(\Z/84\Z)$-generators: | $\begin{bmatrix}7&20\\3&59\end{bmatrix}$, $\begin{bmatrix}37&78\\54&61\end{bmatrix}$, $\begin{bmatrix}67&18\\69&7\end{bmatrix}$, $\begin{bmatrix}73&8\\69&47\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.72.1.r.1 for the level structure with $-I$) |
Cyclic 84-isogeny field degree: | $16$ |
Cyclic 84-torsion field degree: | $192$ |
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 |
---|---|---|---|---|---|---|
6.72.0-6.a.1.1 | $6$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.48.0-84.q.1.6 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
84.48.0-84.q.1.16 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
84.72.0-6.a.1.2 | $84$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
84.288.5-84.f.1.2 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.be.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.dk.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.do.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.fw.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.ge.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.gu.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.gz.1.1 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.dt.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.ig.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bbn.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bcp.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bsq.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.buu.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bzc.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.cal.1.1 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.432.7-252.by.1.1 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.by.1.13 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ch.1.2 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ch.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.dh.1.2 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.dh.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.dq.1.1 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ee.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ee.1.9 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.en.1.1 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.10-252.bv.1.1 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.10-252.bv.1.13 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.13-252.co.1.1 | $252$ | $3$ | $3$ | $13$ | $?$ | not computed |