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: | $\begin{bmatrix}5&50\\6&13\end{bmatrix}$, $\begin{bmatrix}13&16\\33&17\end{bmatrix}$, $\begin{bmatrix}19&52\\60&11\end{bmatrix}$, $\begin{bmatrix}59&12\\6&53\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 84.72.1.m.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.1.2 | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
42.72.0-6.a.1.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.48.0-84.n.1.4 | $84$ | $3$ | $3$ | $0$ | $?$ | full Jacobian |
84.48.0-84.n.1.14 | $84$ | $3$ | $3$ | $0$ | $?$ | 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.a.1.5 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.ba.1.2 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.ds.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.du.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.ei.1.2 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.em.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.fh.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
84.288.5-84.fk.1.3 | $84$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.dc.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.hd.1.3 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bdp.1.7 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bed.1.2 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bhw.1.6 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.biy.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.boq.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
168.288.5-168.bpl.1.5 | $168$ | $2$ | $2$ | $5$ | $?$ | not computed |
252.432.7-252.bv.1.5 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.bv.1.11 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cb.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cb.1.10 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ce.1.3 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.ce.1.10 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cm.1.2 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cr.1.2 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cr.1.11 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.7-252.cw.1.4 | $252$ | $3$ | $3$ | $7$ | $?$ | not computed |
252.432.10-252.bb.1.5 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.10-252.bb.1.11 | $252$ | $3$ | $3$ | $10$ | $?$ | not computed |
252.432.13-252.bq.1.2 | $252$ | $3$ | $3$ | $13$ | $?$ | not computed |