Invariants
Level: | $220$ | $\SL_2$-level: | $20$ | 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 | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | 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: | 20H1 |
Level structure
$\GL_2(\Z/220\Z)$-generators: | $\begin{bmatrix}35&46\\8&3\end{bmatrix}$, $\begin{bmatrix}89&62\\2&9\end{bmatrix}$, $\begin{bmatrix}121&90\\214&147\end{bmatrix}$, $\begin{bmatrix}136&83\\89&60\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 220.72.1.z.2 for the level structure with $-I$) |
Cyclic 220-isogeny field degree: | $24$ |
Cyclic 220-torsion field degree: | $960$ |
Full 220-torsion field degree: | $4224000$ |
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 |
---|---|---|---|---|---|---|
10.72.0-10.a.2.4 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
220.72.0-10.a.2.7 | $220$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
220.288.5-220.f.1.12 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.bg.1.3 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.eq.1.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.fa.1.3 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.ge.1.4 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.gj.1.2 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.hc.1.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.288.5-220.hh.1.2 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |