Invariants
| Level: | $14$ | $\SL_2$-level: | $14$ | Newform level: | $196$ | ||
| Index: | $2016$ | $\PSL_2$-index: | $1008$ | ||||
| Genus: | $49 = 1 + \frac{ 1008 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 72 }{2}$ | ||||||
| Cusps: | $72$ (of which $9$ are rational) | Cusp widths | $14^{72}$ | Cusp orbits | $1^{9}\cdot3^{3}\cdot6^{9}$ | ||
| Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
| Analytic rank: | $1$ | ||||||
| $\Q$-gonality: | $10 \le \gamma \le 18$ | ||||||
| $\overline{\Q}$-gonality: | $10 \le \gamma \le 18$ | ||||||
| Rational cusps: | $9$ | ||||||
| Rational CM points: | none |
Other labels
| Rouse, Sutherland, and Zureick-Brown (RSZB) label: | 14.2016.49.3 |
Level structure
| $\GL_2(\Z/14\Z)$-generators: | $\begin{bmatrix}3&0\\0&1\end{bmatrix}$ |
| $\GL_2(\Z/14\Z)$-subgroup: | $C_6$ |
| Contains $-I$: | no $\quad$ (see 14.1008.49.b.1 for the level structure with $-I$) |
| Cyclic 14-isogeny field degree: | $1$ |
| Cyclic 14-torsion field degree: | $1$ |
| Full 14-torsion field degree: | $6$ |
Jacobian
| Conductor: | $2^{54}\cdot7^{90}$ |
| Simple: | no |
| Squarefree: | no |
| Decomposition: | $1^{11}\cdot2^{13}\cdot4^{3}$ |
| Newforms: | 14.2.a.a$^{4}$, 28.2.e.a$^{2}$, 49.2.a.a$^{3}$, 49.2.c.a$^{3}$, 98.2.a.a$^{2}$, 98.2.a.b$^{2}$, 98.2.c.a$^{2}$, 98.2.c.b$^{2}$, 98.2.c.c$^{2}$, 196.2.a.a, 196.2.a.b, 196.2.a.c, 196.2.e.a, 196.2.e.b |
Rational points
This modular curve has 9 rational cusps but no known non-cuspidal 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 |
|---|---|---|---|---|---|---|
| $X(2)$ | $2$ | $336$ | $168$ | $0$ | $0$ | full Jacobian |
| $X_{\mathrm{arith}}(7)$ | $7$ | $6$ | $6$ | $3$ | $0$ | $1^{10}\cdot2^{12}\cdot4^{3}$ |
This modular curve minimally covers the modular curves listed below.
| Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| $X_1(2,14)$ | $14$ | $7$ | $7$ | $4$ | $0$ | $1^{9}\cdot2^{12}\cdot4^{3}$ |
| 14.288.4-14.a.2.2 | $14$ | $7$ | $7$ | $4$ | $0$ | $1^{9}\cdot2^{12}\cdot4^{3}$ |
| 14.672.15-14.a.1.1 | $14$ | $3$ | $3$ | $15$ | $1$ | $1^{8}\cdot2^{9}\cdot4^{2}$ |
| 14.672.17-14.a.1.1 | $14$ | $3$ | $3$ | $17$ | $1$ | $2^{10}\cdot4^{3}$ |
| 14.672.17-14.d.1.2 | $14$ | $3$ | $3$ | $17$ | $1$ | $1^{8}\cdot2^{8}\cdot4^{2}$ |
| 14.1008.19-14.b.1.1 | $14$ | $2$ | $2$ | $19$ | $0$ | $1^{6}\cdot2^{8}\cdot4^{2}$ |
| 14.1008.19-14.b.1.4 | $14$ | $2$ | $2$ | $19$ | $0$ | $1^{6}\cdot2^{8}\cdot4^{2}$ |
This modular curve is minimally covered by the modular curves in the database listed below.
| Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
|---|---|---|---|---|---|---|
| 28.4032.109-28.b.1.1 | $28$ | $2$ | $2$ | $109$ | $1$ | $2^{2}\cdot4^{6}\cdot8^{2}\cdot16$ |
| 28.4032.109-28.c.1.2 | $28$ | $2$ | $2$ | $109$ | $1$ | $2^{2}\cdot4^{6}\cdot8^{2}\cdot16$ |
| 28.4032.121-28.i.1.4 | $28$ | $2$ | $2$ | $121$ | $10$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 28.4032.121-28.j.1.4 | $28$ | $2$ | $2$ | $121$ | $5$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 28.4032.121-28.k.1.4 | $28$ | $2$ | $2$ | $121$ | $10$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 28.4032.121-28.l.1.3 | $28$ | $2$ | $2$ | $121$ | $6$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 28.4032.133-28.l.1.4 | $28$ | $2$ | $2$ | $133$ | $5$ | $2^{16}\cdot4^{5}\cdot8^{4}$ |
| 28.4032.133-28.m.1.4 | $28$ | $2$ | $2$ | $133$ | $5$ | $2^{16}\cdot4^{5}\cdot8^{4}$ |
| 42.6048.217-42.k.1.2 | $42$ | $3$ | $3$ | $217$ | $14$ | $1^{20}\cdot2^{42}\cdot4^{14}\cdot8$ |
| 42.8064.265-42.c.1.2 | $42$ | $4$ | $4$ | $265$ | $14$ | $1^{54}\cdot2^{63}\cdot4^{9}$ |
| 56.4032.109-56.b.1.2 | $56$ | $2$ | $2$ | $109$ | $1$ | $2^{2}\cdot4^{6}\cdot8^{2}\cdot16$ |
| 56.4032.109-56.c.1.3 | $56$ | $2$ | $2$ | $109$ | $1$ | $2^{2}\cdot4^{6}\cdot8^{2}\cdot16$ |
| 56.4032.121-56.y.1.4 | $56$ | $2$ | $2$ | $121$ | $12$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 56.4032.121-56.z.1.4 | $56$ | $2$ | $2$ | $121$ | $18$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 56.4032.121-56.ba.1.8 | $56$ | $2$ | $2$ | $121$ | $11$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 56.4032.121-56.bb.1.4 | $56$ | $2$ | $2$ | $121$ | $20$ | $1^{16}\cdot2^{20}\cdot4^{4}$ |
| 56.4032.133-56.cd.1.9 | $56$ | $2$ | $2$ | $133$ | $7$ | $2^{16}\cdot4^{5}\cdot8^{4}$ |
| 56.4032.133-56.ce.1.13 | $56$ | $2$ | $2$ | $133$ | $9$ | $2^{16}\cdot4^{5}\cdot8^{4}$ |
| 70.10080.385-70.t.1.2 | $70$ | $5$ | $5$ | $385$ | $51$ | $1^{36}\cdot2^{44}\cdot3^{8}\cdot4^{17}\cdot6^{12}\cdot8^{6}$ |
| 70.12096.433-70.g.1.2 | $70$ | $6$ | $6$ | $433$ | $34$ | $1^{68}\cdot2^{98}\cdot4^{30}$ |
| 70.20160.769-70.p.1.3 | $70$ | $10$ | $10$ | $769$ | $99$ | $1^{104}\cdot2^{142}\cdot3^{8}\cdot4^{47}\cdot6^{12}\cdot8^{6}$ |