Invariants
Level: | $224$ | $\SL_2$-level: | $32$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $3 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $4^{2}\cdot8\cdot32$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 32A3 |
Level structure
$\GL_2(\Z/224\Z)$-generators: | $\begin{bmatrix}64&149\\173&152\end{bmatrix}$, $\begin{bmatrix}70&193\\31&80\end{bmatrix}$, $\begin{bmatrix}74&95\\75&158\end{bmatrix}$, $\begin{bmatrix}168&205\\17&180\end{bmatrix}$, $\begin{bmatrix}202&81\\203&104\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 224.48.3.a.1 for the level structure with $-I$) |
Cyclic 224-isogeny field degree: | $32$ |
Cyclic 224-torsion field degree: | $1536$ |
Full 224-torsion field degree: | $8257536$ |
Rational points
This modular curve has 4 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 |
---|---|---|---|---|---|
16.48.1-16.b.1.6 | $16$ | $2$ | $2$ | $1$ | $0$ |
224.48.1-16.b.1.5 | $224$ | $2$ | $2$ | $1$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
224.192.5-224.d.2.7 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.g.2.6 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.j.1.15 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.l.1.2 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bp.2.12 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bq.1.7 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.br.2.15 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bs.2.10 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bt.2.15 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bu.1.13 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bv.2.15 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bw.2.11 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bx.2.9 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.by.2.25 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.bz.1.5 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.ca.2.13 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.cb.2.9 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.cc.2.13 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.cd.1.5 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.ce.2.11 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.cf.2.3 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.cg.2.6 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.ch.1.3 | $224$ | $2$ | $2$ | $5$ |
224.192.5-224.ci.1.2 | $224$ | $2$ | $2$ | $5$ |