Invariants
Level: | $84$ | $\SL_2$-level: | $12$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $1 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (of which $4$ are rational) | Cusp widths | $2^{2}\cdot4^{2}\cdot6^{2}\cdot12^{2}$ | Cusp orbits | $1^{4}\cdot2^{2}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 12P1 |
Level structure
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
The following modular covers realize this modular curve as a fiber product over $X(1)$.
Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
$X_0(3)$ | $3$ | $12$ | $12$ | $0$ | $0$ | full Jacobian |
28.12.0.g.1 | $28$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
$X_0(12)$ | $12$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
28.12.0.g.1 | $28$ | $4$ | $4$ | $0$ | $0$ | full Jacobian |
42.24.0.b.1 | $42$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
84.24.1.o.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 |
---|---|---|---|---|---|---|
84.96.1.l.1 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1.l.2 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1.l.3 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.96.1.l.4 | $84$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
84.144.5.ca.1 | $84$ | $3$ | $3$ | $5$ | $?$ | not computed |
168.96.1.rp.1 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1.rp.2 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1.rp.3 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.1.rp.4 | $168$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
168.96.3.kq.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.kq.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.ks.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.ks.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.lo.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.lp.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.lw.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.lx.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.me.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.mf.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.mi.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.mj.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.oi.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.oi.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.ok.1 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
168.96.3.ok.2 | $168$ | $2$ | $2$ | $3$ | $?$ | not computed |
252.144.5.k.1 | $252$ | $3$ | $3$ | $5$ | $?$ | not computed |
252.144.9.s.1 | $252$ | $3$ | $3$ | $9$ | $?$ | not computed |
252.144.9.ba.1 | $252$ | $3$ | $3$ | $9$ | $?$ | not computed |