Invariants
Level: | $220$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $72$ | $\PSL_2$-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: | $\begin{bmatrix}17&122\\124&175\end{bmatrix}$, $\begin{bmatrix}23&58\\132&49\end{bmatrix}$, $\begin{bmatrix}80&189\\27&182\end{bmatrix}$, $\begin{bmatrix}109&160\\28&211\end{bmatrix}$, $\begin{bmatrix}173&126\\56&173\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 220.144.1-220.z.2.1, 220.144.1-220.z.2.2, 220.144.1-220.z.2.3, 220.144.1-220.z.2.4, 220.144.1-220.z.2.5, 220.144.1-220.z.2.6, 220.144.1-220.z.2.7, 220.144.1-220.z.2.8, 220.144.1-220.z.2.9, 220.144.1-220.z.2.10, 220.144.1-220.z.2.11, 220.144.1-220.z.2.12, 220.144.1-220.z.2.13, 220.144.1-220.z.2.14, 220.144.1-220.z.2.15, 220.144.1-220.z.2.16 |
Cyclic 220-isogeny field degree: | $24$ |
Cyclic 220-torsion field degree: | $960$ |
Full 220-torsion field degree: | $8448000$ |
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 |
---|---|---|---|---|---|---|
$X_{\pm1}(10)$ | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
220.36.0.b.2 | $220$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
220.36.1.f.1 | $220$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
220.144.5.f.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.bg.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.eq.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.fa.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.ge.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.gj.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.hc.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.144.5.hh.1 | $220$ | $2$ | $2$ | $5$ | $?$ | not computed |
220.360.13.v.1 | $220$ | $5$ | $5$ | $13$ | $?$ | not computed |