Invariants
Level: | $170$ | $\SL_2$-level: | $10$ | Newform level: | $1$ | ||
Index: | $120$ | $\PSL_2$-index: | $120$ | ||||
Genus: | $5 = 1 + \frac{ 120 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (none of which are rational) | Cusp widths | $10^{12}$ | Cusp orbits | $2^{2}\cdot8$ | ||
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: | 10A5 |
Level structure
$\GL_2(\Z/170\Z)$-generators: | $\begin{bmatrix}17&140\\105&87\end{bmatrix}$, $\begin{bmatrix}56&147\\131&115\end{bmatrix}$, $\begin{bmatrix}62&119\\137&30\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 170.240.5-170.q.1.1, 170.240.5-170.q.1.2, 170.240.5-170.q.1.3, 170.240.5-170.q.1.4 |
Cyclic 170-isogeny field degree: | $54$ |
Cyclic 170-torsion field degree: | $3456$ |
Full 170-torsion field degree: | $1880064$ |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
10.60.2.c.1 | $10$ | $2$ | $2$ | $2$ | $0$ |
85.60.0.a.1 | $85$ | $2$ | $2$ | $0$ | $?$ |
170.24.1.e.1 | $170$ | $5$ | $5$ | $1$ | $?$ |
170.24.1.e.2 | $170$ | $5$ | $5$ | $1$ | $?$ |
170.60.3.e.1 | $170$ | $2$ | $2$ | $3$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
170.360.13.i.1 | $170$ | $3$ | $3$ | $13$ |