Invariants
Level: | $220$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $5 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 8 }{2}$ | ||||||
Cusps: | $8$ (none of which are rational) | Cusp widths | $4^{4}\cdot20^{4}$ | Cusp orbits | $2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 8$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 5$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20D5 |
Level structure
$\GL_2(\Z/220\Z)$-generators: | $\begin{bmatrix}61&113\\170&39\end{bmatrix}$, $\begin{bmatrix}149&193\\143&194\end{bmatrix}$, $\begin{bmatrix}208&169\\59&213\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 220.96.5.n.1 for the level structure with $-I$) |
Cyclic 220-isogeny field degree: | $72$ |
Cyclic 220-torsion field degree: | $5760$ |
Full 220-torsion field degree: | $3168000$ |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
20.96.3-20.i.2.6 | $20$ | $2$ | $2$ | $3$ | $0$ |
220.48.1-220.j.2.2 | $220$ | $4$ | $4$ | $1$ | $?$ |
220.96.3-20.i.2.4 | $220$ | $2$ | $2$ | $3$ | $?$ |