Invariants
| Level: | $25$ | $\SL_2$-level: | $25$ | Newform level: | $625$ | ||
| Index: | $750$ | $\PSL_2$-index: | $750$ | ||||
| Genus: | $48 = 1 + \frac{ 750 }{12} - \frac{ 2 }{4} - \frac{ 0 }{3} - \frac{ 30 }{2}$ | ||||||
| Cusps: | $30$ (of which $2$ are rational) | Cusp widths | $25^{30}$ | Cusp orbits | $1^{2}\cdot4^{2}\cdot20$ | ||
| Elliptic points: | $2$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $18$ | ||||||
| $\Q$-gonality: | $13 \le \gamma \le 20$ | ||||||
| $\overline{\Q}$-gonality: | $13 \le \gamma \le 20$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 25.750.48.1 |
Level structure
| $\GL_2(\Z/25\Z)$-generators: | $\begin{bmatrix}2&0\\0&1\end{bmatrix}$, $\begin{bmatrix}3&0\\0&3\end{bmatrix}$ |
| $\GL_2(\Z/25\Z)$-subgroup: | $C_{20}^2$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 25-isogeny field degree: | $1$ |
| Cyclic 25-torsion field degree: | $20$ |
| Full 25-torsion field degree: | $400$ |
Jacobian
| Conductor: | $5^{176}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $2^{8}\cdot4^{2}\cdot8^{3}$ |
| Newforms: | 125.2.a.a$^{2}$, 125.2.a.b$^{2}$, 125.2.a.c$^{2}$, 625.2.a.a, 625.2.a.b, 625.2.a.c, 625.2.a.d, 625.2.a.e, 625.2.a.f, 625.2.a.g |
Rational points
This modular curve has 2 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 25.150.8.a.1 | $25$ | $5$ | $5$ | $8$ | $2$ | $2^{6}\cdot4\cdot8^{3}$ |
| $X_{\mathrm{sp}}^+(25)$ | $25$ | $2$ | $2$ | $22$ | $16$ | $2^{3}\cdot4\cdot8^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 25.1500.96.e.1 | $25$ | $2$ | $2$ | $96$ | $18$ | $4^{6}\cdot8\cdot16$ |
| 25.3750.236.a.1 | $25$ | $5$ | $5$ | $236$ | $22$ | $4^{15}\cdot8^{2}\cdot16^{7}$ |
| 25.3750.236.b.1 | $25$ | $5$ | $5$ | $236$ | $22$ | $4^{15}\cdot8^{2}\cdot16^{7}$ |
| 25.3750.236.c.1 | $25$ | $5$ | $5$ | $236$ | $94$ | $2^{30}\cdot4^{4}\cdot8^{14}$ |
| 50.1500.110.a.1 | $50$ | $2$ | $2$ | $110$ | $18$ | $2^{3}\cdot4^{5}\cdot8\cdot12\cdot16$ |
| 50.1500.111.b.1 | $50$ | $2$ | $2$ | $111$ | $40$ | $1^{7}\cdot2^{6}\cdot4^{2}\cdot6^{2}\cdot8^{3}$ |
| 50.1500.111.e.1 | $50$ | $2$ | $2$ | $111$ | $40$ | $1^{7}\cdot2^{6}\cdot4^{2}\cdot6^{2}\cdot8^{3}$ |
| 50.2250.158.a.1 | $50$ | $3$ | $3$ | $158$ | $54$ | $1^{6}\cdot2^{20}\cdot4^{10}\cdot8^{3}$ |
| 125.3750.288.a.1 | $125$ | $5$ | $5$ | $288$ | $?$ | not computed |