Invariants
Level: | $240$ | $\SL_2$-level: | $16$ | Newform level: | $1$ | ||
Index: | $48$ | $\PSL_2$-index: | $24$ | ||||
Genus: | $1 = 1 + \frac{ 24 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 4 }{2}$ | ||||||
Cusps: | $4$ (all of which are rational) | Cusp widths | $2^{2}\cdot4\cdot16$ | Cusp orbits | $1^{4}$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16A1 |
Level structure
$\GL_2(\Z/240\Z)$-generators: | $\begin{bmatrix}22&231\\179&130\end{bmatrix}$, $\begin{bmatrix}76&89\\221&8\end{bmatrix}$, $\begin{bmatrix}98&11\\87&230\end{bmatrix}$, $\begin{bmatrix}137&102\\208&107\end{bmatrix}$, $\begin{bmatrix}146&231\\77&64\end{bmatrix}$, $\begin{bmatrix}194&239\\115&62\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 80.24.1.a.1 for the level structure with $-I$) |
Cyclic 240-isogeny field degree: | $48$ |
Cyclic 240-torsion field degree: | $3072$ |
Full 240-torsion field degree: | $11796480$ |
Jacobian
Conductor: | $?$ |
Simple: | yes |
Squarefree: | yes |
Decomposition: | $1$ |
Newforms: | not computed |
Rational points
This modular curve is an elliptic curve, but the rank has not been computed
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
24.24.0-8.n.1.7 | $24$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
240.24.0-8.n.1.4 | $240$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus | Rank | Kernel decomposition |
---|---|---|---|---|---|---|
240.96.1-80.a.2.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.d.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.g.1.19 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.i.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bq.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bq.2.4 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bq.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.br.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.br.2.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bs.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bs.2.3 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bs.1.21 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bt.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bt.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bu.1.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bu.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bu.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bv.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bv.2.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bw.1.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bw.2.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.bw.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bx.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.bx.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.ch.1.1 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.ci.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.cl.1.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-80.cm.1.13 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.es.1.2 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.es.2.11 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.et.1.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.et.2.28 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.eu.1.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.eu.2.15 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ev.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ev.2.20 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ew.1.26 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ew.2.28 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ex.1.7 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ex.2.14 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ey.1.30 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ey.2.32 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ez.1.5 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.ez.2.6 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.he.1.29 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hg.1.9 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hi.1.29 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.96.1-240.hk.1.25 | $240$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
240.144.5-240.a.1.11 | $240$ | $3$ | $3$ | $5$ | $?$ | not computed |
240.192.5-240.bvv.1.91 | $240$ | $4$ | $4$ | $5$ | $?$ | not computed |
240.240.9-80.e.1.14 | $240$ | $5$ | $5$ | $9$ | $?$ | not computed |
240.288.9-80.m.1.25 | $240$ | $6$ | $6$ | $9$ | $?$ | not computed |
240.480.17-80.di.1.10 | $240$ | $10$ | $10$ | $17$ | $?$ | not computed |