Invariants
Level: | $240$ | $\SL_2$-level: | $48$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (none of which are rational) | Cusp widths | $1^{4}\cdot2^{2}\cdot3^{4}\cdot6^{2}\cdot8^{2}\cdot24^{2}$ | Cusp orbits | $2^{8}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 96$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 24J1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}5&162\\186&53\end{bmatrix}$, $\begin{bmatrix}40&159\\17&14\end{bmatrix}$, $\begin{bmatrix}94&151\\135&158\end{bmatrix}$, $\begin{bmatrix}137&0\\106&127\end{bmatrix}$, $\begin{bmatrix}143&110\\112&93\end{bmatrix}$, $\begin{bmatrix}148&103\\87&188\end{bmatrix}$, $\begin{bmatrix}196&9\\71&38\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.se.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $12$ |
Cyclic 240-torsion field degree: | $384$ |
Full 240-torsion field degree: | $2949120$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
48.96.1-24.ir.1.17 | $48$ | $2$ | $2$ | $1$ | $0$ | dimension zero |
240.96.1-24.ir.1.22 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
240.384.5-120.qy.4.20 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.rk.3.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.sa.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.sb.3.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vm.3.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vo.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vu.2.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vw.3.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bep.2.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bep.2.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beq.3.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beq.3.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.ber.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.ber.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bes.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bes.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bet.2.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bet.2.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beu.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beu.3.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bev.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bev.1.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bew.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bew.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bex.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bex.1.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bey.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bey.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bez.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bez.3.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfa.2.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfa.2.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfb.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfb.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfc.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfc.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfd.3.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfd.3.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfe.2.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfe.2.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfy.3.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bga.3.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bgg.4.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bgi.1.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bik.2.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bim.4.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bis.4.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.biu.2.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckb.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckb.3.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckc.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckc.3.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckr.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckr.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cks.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cks.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clg.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clg.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clh.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clh.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cli.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cli.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clj.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clj.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clo.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clo.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clp.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clp.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clq.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clq.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clr.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clr.1.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clw.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clw.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clx.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clx.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cly.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cly.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clz.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clz.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cme.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cme.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmf.1.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmf.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmg.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmg.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmh.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmh.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmn.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmn.3.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmo.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmo.3.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmv.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmv.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmw.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmw.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.9-240.ela.1.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.ela.1.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.elb.1.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.elb.1.37 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnm.1.2 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnm.1.34 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnn.1.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnn.1.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyo.1.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyo.1.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyp.1.2 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyp.1.34 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzu.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzu.2.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzv.2.2 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzv.2.34 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |