Invariants
Level: | $260$ | $\SL_2$-level: | $20$ | Newform level: | $1$ | ||
Index: | $144$ | $\PSL_2$-index: | $72$ | ||||
Genus: | $1 = 1 + \frac{ 72 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $2$ are rational) | Cusp widths | $1^{4}\cdot4^{2}\cdot5^{4}\cdot20^{2}$ | Cusp orbits | $1^{2}\cdot2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2$ | ||||||
$\overline{\Q}$-gonality: | $2$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 20H1 |
Level structure
$\GL_2(\Z/260\Z)$-generators: | $\begin{bmatrix}20&69\\99&100\end{bmatrix}$, $\begin{bmatrix}193&258\\230&71\end{bmatrix}$, $\begin{bmatrix}196&193\\217&32\end{bmatrix}$, $\begin{bmatrix}250&249\\87&52\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 260.72.1.ba.2 for the level structure with $-I$) |
Cyclic 260-isogeny field degree: | $28$ |
Cyclic 260-torsion field degree: | $1344$ |
Full 260-torsion field degree: | $8386560$ |
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 |
---|---|---|---|---|---|---|
10.72.0-10.a.2.4 | $10$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
260.72.0-10.a.2.12 | $260$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
260.288.5-260.e.1.4 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.be.1.1 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.eu.1.1 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.ey.1.3 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.gg.1.1 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.gi.1.3 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.hd.1.1 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |
260.288.5-260.hg.1.4 | $260$ | $2$ | $2$ | $5$ | $?$ | not computed |