Invariants
| Level: | $35$ | $\SL_2$-level: | $35$ | Newform level: | $1225$ | ||
| Index: | $840$ | $\PSL_2$-index: | $840$ | ||||
| Genus: | $59 = 1 + \frac{ 840 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 24 }{2}$ | ||||||
| Cusps: | $24$ (none of which are rational) | Cusp widths | $35^{24}$ | Cusp orbits | $24$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $26$ | ||||||
| $\Q$-gonality: | $16 \le \gamma \le 40$ | ||||||
| $\overline{\Q}$-gonality: | $16 \le \gamma \le 40$ | ||||||
| Rational cusps: | $0$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 35.840.59.19 |
Level structure
| $\GL_2(\Z/35\Z)$-generators: | $\begin{bmatrix}31&34\\6&32\end{bmatrix}$, $\begin{bmatrix}34&18\\32&16\end{bmatrix}$ |
| Contains $-I$: | yes |
| Quadratic refinements: | none in database |
| Cyclic 35-isogeny field degree: | $48$ |
| Cyclic 35-torsion field degree: | $1152$ |
| Full 35-torsion field degree: | $1152$ |
Jacobian
| Conductor: | $5^{116}\cdot7^{118}$ |
| Simple: | no |
| Squarefree: | yes |
| Decomposition: | $1^{11}\cdot2^{12}\cdot3^{4}\cdot4^{3}$ |
| Newforms: | 49.2.a.a, 1225.2.a.a, 1225.2.a.b, 1225.2.a.ba, 1225.2.a.bb, 1225.2.a.bc, 1225.2.a.c, 1225.2.a.d, 1225.2.a.e, 1225.2.a.f, 1225.2.a.g, 1225.2.a.h, 1225.2.a.i, 1225.2.a.j, 1225.2.a.k, 1225.2.a.l, 1225.2.a.m, 1225.2.a.n, 1225.2.a.o, 1225.2.a.p, 1225.2.a.q, 1225.2.a.r, 1225.2.a.s, 1225.2.a.t, 1225.2.a.u, 1225.2.a.v, 1225.2.a.w, 1225.2.a.x, 1225.2.a.y, 1225.2.a.z |
Rational points
This modular curve has no real points, and therefore no rational points.
Modular covers
The following modular covers realize this modular curve as a fiber product over $X(1)$.
| Factor curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}(5)$ | $5$ | $42$ | $42$ | $0$ | $0$ | full Jacobian |
| $X_{\mathrm{ns}}(7)$ | $7$ | $20$ | $20$ | $1$ | $0$ | $1^{10}\cdot2^{12}\cdot3^{4}\cdot4^{3}$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_{\mathrm{ns}}^+(35)$ | $35$ | $2$ | $2$ | $26$ | $26$ | $1^{7}\cdot2^{6}\cdot3^{2}\cdot4^{2}$ |
| 35.420.29.c.1 | $35$ | $2$ | $2$ | $29$ | $13$ | $1^{6}\cdot2^{5}\cdot3^{2}\cdot4^{2}$ |
| 35.420.30.a.1 | $35$ | $2$ | $2$ | $30$ | $13$ | $1^{9}\cdot2^{7}\cdot3^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 35.2520.175.e.1 | $35$ | $3$ | $3$ | $175$ | $72$ | $1^{28}\cdot2^{30}\cdot3^{4}\cdot4^{4}$ |
| 35.2520.175.i.1 | $35$ | $3$ | $3$ | $175$ | $26$ | $2^{14}\cdot4^{15}\cdot6^{2}\cdot8^{2}$ |
| $X_{\mathrm{ns}}(70)$ | $70$ | $2$ | $2$ | $129$ | $57$ | $1^{26}\cdot2^{4}\cdot3^{4}\cdot4^{6}$ |
| 70.1680.129.ce.1 | $70$ | $2$ | $2$ | $129$ | $54$ | $1^{26}\cdot2^{4}\cdot3^{4}\cdot4^{6}$ |
| 70.1680.129.dh.1 | $70$ | $2$ | $2$ | $129$ | $58$ | $1^{26}\cdot2^{4}\cdot3^{4}\cdot4^{6}$ |
| 70.1680.129.dl.1 | $70$ | $2$ | $2$ | $129$ | $55$ | $1^{26}\cdot2^{4}\cdot3^{4}\cdot4^{6}$ |
| 70.2520.187.a.1 | $70$ | $3$ | $3$ | $187$ | $75$ | $1^{48}\cdot2^{24}\cdot3^{4}\cdot4^{5}$ |