Invariants
Level: | $275$ | $\SL_2$-level: | $25$ | Newform level: | $1$ | ||
Index: | $300$ | $\PSL_2$-index: | $300$ | ||||
Genus: | $12 = 1 + \frac{ 300 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 28 }{2}$ | ||||||
Cusps: | $28$ (none of which are rational) | Cusp widths | $1^{10}\cdot5^{8}\cdot25^{10}$ | Cusp orbits | $4^{2}\cdot5^{2}\cdot10$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $4 \le \gamma \le 22$ | ||||||
$\overline{\Q}$-gonality: | $4 \le \gamma \le 12$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 25B12 |
Level structure
$\GL_2(\Z/275\Z)$-generators: | $\begin{bmatrix}14&267\\242&239\end{bmatrix}$, $\begin{bmatrix}186&9\\185&262\end{bmatrix}$, $\begin{bmatrix}219&123\\265&236\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | none in database |
Cyclic 275-isogeny field degree: | $12$ |
Cyclic 275-torsion field degree: | $2400$ |
Full 275-torsion field degree: | $13200000$ |
Rational points
This modular curve has no $\Q_p$ points for $p=2,23$, and therefore no rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
25.60.0.a.2 | $25$ | $5$ | $5$ | $0$ | $0$ |
275.150.4.t.1 | $275$ | $2$ | $2$ | $4$ | $?$ |