Invariants
Level: | $72$ | $\SL_2$-level: | $36$ | 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 | $1^{6}\cdot4^{3}\cdot9^{2}\cdot36$ | 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: | 36C1 |
Level structure
$\GL_2(\Z/72\Z)$-generators: | $\begin{bmatrix}15&68\\10&37\end{bmatrix}$, $\begin{bmatrix}18&25\\41&38\end{bmatrix}$, $\begin{bmatrix}41&56\\30&1\end{bmatrix}$, $\begin{bmatrix}71&26\\12&1\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 72.72.1.j.1 for the level structure with $-I$) |
Cyclic 72-isogeny field degree: | $4$ |
Cyclic 72-torsion field degree: | $96$ |
Full 72-torsion field degree: | $41472$ |
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 |
---|---|---|---|---|---|---|
24.48.0-24.cd.1.14 | $24$ | $3$ | $3$ | $0$ | $0$ | full Jacobian |
36.72.0-18.a.1.12 | $36$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
72.72.0-18.a.1.8 | $72$ | $2$ | $2$ | $0$ | $?$ | 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 |
---|---|---|---|---|---|---|
72.288.5-72.d.1.11 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.i.1.7 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.s.1.7 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.u.1.5 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.bs.1.7 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.bu.1.7 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.cb.1.7 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.288.5-72.cd.1.1 | $72$ | $2$ | $2$ | $5$ | $?$ | not computed |
72.432.7-72.ct.1.13 | $72$ | $3$ | $3$ | $7$ | $?$ | not computed |
72.432.7-72.ct.2.10 | $72$ | $3$ | $3$ | $7$ | $?$ | not computed |
72.432.7-72.et.1.12 | $72$ | $3$ | $3$ | $7$ | $?$ | not computed |
72.432.10-72.bi.1.13 | $72$ | $3$ | $3$ | $10$ | $?$ | not computed |
216.432.7-216.h.1.5 | $216$ | $3$ | $3$ | $7$ | $?$ | not computed |
216.432.10-216.t.1.12 | $216$ | $3$ | $3$ | $10$ | $?$ | not computed |
216.432.13-216.v.1.12 | $216$ | $3$ | $3$ | $13$ | $?$ | not computed |