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: | $\begin{bmatrix}74&171\\183&206\end{bmatrix}$, $\begin{bmatrix}138&91\\115&114\end{bmatrix}$, $\begin{bmatrix}176&111\\231&128\end{bmatrix}$, $\begin{bmatrix}194&81\\73&130\end{bmatrix}$, $\begin{bmatrix}205&108\\38&131\end{bmatrix}$, $\begin{bmatrix}210&199\\229&132\end{bmatrix}$, $\begin{bmatrix}212&107\\199&0\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 120.96.1.se.3 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.1.24 | $240$ | $2$ | $2$ | $1$ | $?$ | 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.2.29 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.rk.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.sa.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.sb.2.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vm.4.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vo.2.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vu.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.vw.4.11 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bep.4.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bep.4.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beq.4.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beq.4.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.ber.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.ber.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bes.3.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bes.3.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bet.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bet.4.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beu.4.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.beu.4.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bev.2.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bev.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bew.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bew.3.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bex.3.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bex.3.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bey.2.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bey.2.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bez.4.2 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bez.4.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfa.4.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfa.4.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfb.3.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfb.3.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfc.2.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfc.2.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfd.4.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfd.4.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfe.4.6 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfe.4.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bfy.1.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bga.4.14 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bgg.2.10 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bgi.2.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bik.1.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bim.3.16 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.bis.3.12 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-120.biu.1.8 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckb.1.3 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckb.1.4 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckc.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckc.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckr.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.ckr.3.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cks.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cks.3.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clg.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clg.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clh.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clh.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cli.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cli.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clj.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clj.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clo.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clo.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clp.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clp.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clq.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clq.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clr.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clr.2.33 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clw.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clw.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clx.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clx.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cly.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cly.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clz.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.clz.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cme.3.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cme.3.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmf.2.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmf.2.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmg.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmg.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmh.4.1 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmh.4.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmn.1.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmn.1.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmo.1.5 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmo.1.7 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmv.3.17 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmv.3.25 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmw.3.9 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.5-240.cmw.3.13 | $240$ | $2$ | $2$ | $5$ | $?$ | not computed |
240.384.9-240.ela.2.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.ela.2.37 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.elb.2.9 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.elb.2.41 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnm.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnm.2.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnn.2.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fnn.2.37 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyo.2.5 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyo.2.37 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyp.2.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fyp.2.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzu.1.3 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzu.1.35 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzv.1.2 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |
240.384.9-240.fzv.1.34 | $240$ | $2$ | $2$ | $9$ | $?$ | not computed |