Invariants
| Level: | $17$ | $\SL_2$-level: | $17$ | Newform level: | $289$ | ||
| Index: | $4896$ | $\PSL_2$-index: | $2448$ | ||||
| Genus: | $133 = 1 + \frac{ 2448 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 144 }{2}$ | ||||||
| Cusps: | $144$ (of which $8$ are rational) | Cusp widths | $17^{144}$ | Cusp orbits | $1^{8}\cdot8\cdot16^{8}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $6$ | ||||||
| $\Q$-gonality: | $25 \le \gamma \le 68$ | ||||||
| $\overline{\Q}$-gonality: | $25 \le \gamma \le 68$ | ||||||
| Rational cusps: | $8$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 17.4896.133.1 |
| Sutherland (S) label: | 17Cs.1.1 |
Level structure
| $\GL_2(\Z/17\Z)$-generators: | $\begin{bmatrix}1&0\\0&6\end{bmatrix}$ |
| $\GL_2(\Z/17\Z)$-subgroup: | $C_{16}$ |
| Contains $-I$: | no $\quad$ (see 17.2448.133.e.1 for the level structure with $-I$) |
| Cyclic 17-isogeny field degree: | $1$ |
| Cyclic 17-torsion field degree: | $1$ |
| Full 17-torsion field degree: | $16$ |
Jacobian
| Conductor: | $17^{256}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{3}\cdot2^{3}\cdot3^{2}\cdot4^{9}\cdot6\cdot8^{3}\cdot12\cdot16\cdot24$ |
| Newforms: | 17.2.a.a$^{2}$, 17.2.d.a$^{2}$, 289.2.a.a, 289.2.a.b, 289.2.a.c, 289.2.a.d, 289.2.a.e, 289.2.a.f, 289.2.b.a, 289.2.b.b, 289.2.b.c, 289.2.b.d, 289.2.c.a, 289.2.c.b, 289.2.c.c, 289.2.c.d, 289.2.d.a, 289.2.d.b, 289.2.d.c, 289.2.d.d, 289.2.d.e, 289.2.d.f |
Rational points
This modular curve has 8 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 |
|---|---|---|---|---|---|---|
| 17.288.5-17.d.1.2 | $17$ | $17$ | $17$ | $5$ | $0$ | $1^{2}\cdot2^{3}\cdot3^{2}\cdot4^{8}\cdot6\cdot8^{3}\cdot12\cdot16\cdot24$ |
| $X_1(17)$ | $17$ | $17$ | $17$ | $5$ | $0$ | $1^{2}\cdot2^{3}\cdot3^{2}\cdot4^{8}\cdot6\cdot8^{3}\cdot12\cdot16\cdot24$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 34.9792.337-34.g.1.1 | $34$ | $2$ | $2$ | $337$ | $15$ | $2^{10}\cdot3^{2}\cdot4^{14}\cdot6\cdot8^{4}\cdot12\cdot16^{3}\cdot24$ |
| 34.9792.337-34.j.1.1 | $34$ | $2$ | $2$ | $337$ | $15$ | $2^{10}\cdot3^{2}\cdot4^{14}\cdot6\cdot8^{4}\cdot12\cdot16^{3}\cdot24$ |
| 34.14688.469-34.e.1.1 | $34$ | $3$ | $3$ | $469$ | $22$ | $1^{6}\cdot2^{19}\cdot3^{6}\cdot4^{17}\cdot6^{3}\cdot8^{8}\cdot12^{3}\cdot16\cdot24^{3}$ |
| 51.14688.541-51.q.1.1 | $51$ | $3$ | $3$ | $541$ | $31$ | $1^{10}\cdot2^{9}\cdot3^{2}\cdot4^{23}\cdot6^{3}\cdot8^{16}\cdot12^{2}\cdot16\cdot24^{2}\cdot48$ |
| 51.19584.673-51.i.1.2 | $51$ | $4$ | $4$ | $673$ | $29$ | $1^{10}\cdot2^{13}\cdot3^{4}\cdot4^{20}\cdot6^{4}\cdot8^{21}\cdot12^{3}\cdot16^{4}\cdot24^{3}\cdot48$ |
| 68.9792.337-68.bb.1.2 | $68$ | $2$ | $2$ | $337$ | $15$ | $2^{10}\cdot3^{2}\cdot4^{14}\cdot6\cdot8^{4}\cdot12\cdot16^{3}\cdot24$ |
| 68.9792.337-68.bk.1.1 | $68$ | $2$ | $2$ | $337$ | $15$ | $2^{10}\cdot3^{2}\cdot4^{14}\cdot6\cdot8^{4}\cdot12\cdot16^{3}\cdot24$ |
| 68.19584.745-68.db.1.1 | $68$ | $4$ | $4$ | $745$ | $56$ | $1^{8}\cdot2^{36}\cdot3^{4}\cdot4^{20}\cdot6^{4}\cdot8^{13}\cdot12^{10}\cdot16^{3}\cdot24^{4}\cdot48$ |
| 289.83232.3269-289.e.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.f.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.m.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.o.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.t.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.w.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bc.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bd.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bj.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bm.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bs.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.bu.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.ca.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.cb.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.ch.1.2 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.ck.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3269-289.cq.1.1 | $289$ | $17$ | $17$ | $3269$ | $?$ | not computed |
| 289.83232.3333-289.d.1.1 | $289$ | $17$ | $17$ | $3333$ | $?$ | not computed |
| 289.83232.3333-289.d.2.1 | $289$ | $17$ | $17$ | $3333$ | $?$ | not computed |