Invariants
| Level: | $25$ | $\SL_2$-level: | $25$ | Newform level: | $125$ | ||
| Index: | $600$ | $\PSL_2$-index: | $300$ | ||||
| Genus: | $16 = 1 + \frac{ 300 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 20 }{2}$ | ||||||
| Cusps: | $20$ (of which $2$ are rational) | Cusp widths | $5^{10}\cdot25^{10}$ | Cusp orbits | $1^{2}\cdot2\cdot4^{4}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $2$ | ||||||
| $\Q$-gonality: | $5$ | ||||||
| $\overline{\Q}$-gonality: | $5$ | ||||||
| Rational cusps: | $2$ | ||||||
| Rational CM points: | none |
Other labels
| Cummins and Pauli (CP) label: | 25A16 |
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 25.600.16.1 |
Level structure
| $\GL_2(\Z/25\Z)$-generators: | $\begin{bmatrix}1&0\\0&22\end{bmatrix}$, $\begin{bmatrix}11&5\\0&3\end{bmatrix}$ |
| $\GL_2(\Z/25\Z)$-subgroup: | $F_5\times C_5^2$ |
| Contains $-I$: | no $\quad$ (see 25.300.16.a.1 for the level structure with $-I$) |
| Cyclic 25-isogeny field degree: | $1$ |
| Cyclic 25-torsion field degree: | $5$ |
| Full 25-torsion field degree: | $500$ |
Jacobian
| Conductor: | $5^{48}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $2^{2}\cdot4^{3}$ |
| Newforms: | 125.2.a.a, 125.2.a.b, 125.2.a.c, 125.2.b.a, 125.2.b.b |
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 |
|---|---|---|---|---|---|---|
| $X_{\mathrm{arith}}(5)$ | $5$ | $5$ | $5$ | $0$ | $0$ | full Jacobian |
| 25.120.0-25.a.1.2 | $25$ | $5$ | $5$ | $0$ | $0$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 25.3000.76-25.a.1.2 | $25$ | $5$ | $5$ | $76$ | $2$ | $4^{3}\cdot8^{4}\cdot16$ |
| 25.3000.76-25.b.2.1 | $25$ | $5$ | $5$ | $76$ | $2$ | $4^{3}\cdot8^{4}\cdot16$ |
| 25.3000.76-25.c.1.2 | $25$ | $5$ | $5$ | $76$ | $2$ | $4^{3}\cdot8^{4}\cdot16$ |
| 25.3000.76-25.d.2.1 | $25$ | $5$ | $5$ | $76$ | $2$ | $4^{3}\cdot8^{4}\cdot16$ |
| 25.3000.76-25.e.1.2 | $25$ | $5$ | $5$ | $76$ | $14$ | $2^{6}\cdot4^{2}\cdot8^{5}$ |
| 25.3000.96-25.e.1.2 | $25$ | $5$ | $5$ | $96$ | $18$ | $2^{6}\cdot4^{5}\cdot8^{4}\cdot16$ |
| 50.1200.41-50.a.2.2 | $50$ | $2$ | $2$ | $41$ | $4$ | $1^{5}\cdot2^{4}\cdot4^{3}$ |
| 50.1200.41-50.b.2.2 | $50$ | $2$ | $2$ | $41$ | $4$ | $1^{5}\cdot2^{4}\cdot4^{3}$ |
| 50.1800.56-50.a.2.2 | $50$ | $3$ | $3$ | $56$ | $6$ | $1^{4}\cdot2^{8}\cdot4^{5}$ |
| 125.3000.96-125.a.1.2 | $125$ | $5$ | $5$ | $96$ | $?$ | not computed |