Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $96$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $1 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 16 }{2}$ | ||||||
Cusps: | $16$ (of which $4$ are rational) | Cusp widths | $4^{8}\cdot8^{8}$ | Cusp orbits | $1^{4}\cdot4^{3}$ | ||
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: | 8K1 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}15&140\\64&47\end{bmatrix}$, $\begin{bmatrix}93&84\\40&127\end{bmatrix}$, $\begin{bmatrix}121&116\\12&103\end{bmatrix}$, $\begin{bmatrix}129&4\\112&7\end{bmatrix}$, $\begin{bmatrix}137&40\\44&103\end{bmatrix}$ |
Contains $-I$: | yes |
Quadratic refinements: | 152.192.1-152.x.2.1, 152.192.1-152.x.2.2, 152.192.1-152.x.2.3, 152.192.1-152.x.2.4, 152.192.1-152.x.2.5, 152.192.1-152.x.2.6, 152.192.1-152.x.2.7, 152.192.1-152.x.2.8, 152.192.1-152.x.2.9, 152.192.1-152.x.2.10, 152.192.1-152.x.2.11, 152.192.1-152.x.2.12, 304.192.1-152.x.2.1, 304.192.1-152.x.2.2, 304.192.1-152.x.2.3, 304.192.1-152.x.2.4, 304.192.1-152.x.2.5, 304.192.1-152.x.2.6, 304.192.1-152.x.2.7, 304.192.1-152.x.2.8 |
Cyclic 152-isogeny field degree: | $40$ |
Cyclic 152-torsion field degree: | $1440$ |
Full 152-torsion field degree: | $1969920$ |
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 |
---|---|---|---|---|---|---|
8.48.0.c.1 | $8$ | $2$ | $2$ | $0$ | $0$ | full Jacobian |
152.48.0.b.1 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.48.0.u.2 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.48.0.v.2 | $152$ | $2$ | $2$ | $0$ | $?$ | full Jacobian |
152.48.1.o.2 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.48.1.be.1 | $152$ | $2$ | $2$ | $1$ | $?$ | dimension zero |
152.48.1.bf.1 | $152$ | $2$ | $2$ | $1$ | $?$ | 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 |
---|---|---|---|---|---|---|
152.192.5.x.1 | $152$ | $2$ | $2$ | $5$ | $?$ | not computed |
152.192.5.y.1 | $152$ | $2$ | $2$ | $5$ | $?$ | not computed |
152.192.5.ba.1 | $152$ | $2$ | $2$ | $5$ | $?$ | not computed |
152.192.5.bb.4 | $152$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.a.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.g.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.p.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.r.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.cq.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.cs.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.db.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |
304.192.5.dh.2 | $304$ | $2$ | $2$ | $5$ | $?$ | not computed |