Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | Newform level: | $1$ | ||
Index: | $192$ | $\PSL_2$-index: | $96$ | ||||
Genus: | $3 = 1 + \frac{ 96 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 12 }{2}$ | ||||||
Cusps: | $12$ (of which $4$ are rational) | Cusp widths | $8^{12}$ | Cusp orbits | $1^{4}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
Analytic rank: | not computed | ||||||
$\Q$-gonality: | $2 \le \gamma \le 3$ | ||||||
$\overline{\Q}$-gonality: | $2 \le \gamma \le 3$ | ||||||
Rational cusps: | $4$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8B3 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}41&80\\140&145\end{bmatrix}$, $\begin{bmatrix}57&68\\40&51\end{bmatrix}$, $\begin{bmatrix}57&140\\52&33\end{bmatrix}$, $\begin{bmatrix}105&88\\52&119\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.96.3.x.1 for the level structure with $-I$) |
Cyclic 152-isogeny field degree: | $40$ |
Cyclic 152-torsion field degree: | $720$ |
Full 152-torsion field degree: | $984960$ |
Rational points
This modular curve has 4 rational cusps but no known non-cuspidal rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.96.0-8.c.1.1 | $8$ | $2$ | $2$ | $0$ | $0$ |
152.96.0-8.c.1.8 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.96.1-152.o.1.1 | $152$ | $2$ | $2$ | $1$ | $?$ |
152.96.1-152.o.1.7 | $152$ | $2$ | $2$ | $1$ | $?$ |
152.96.2-152.a.1.1 | $152$ | $2$ | $2$ | $2$ | $?$ |
152.96.2-152.a.1.3 | $152$ | $2$ | $2$ | $2$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
152.384.5-152.ba.1.1 | $152$ | $2$ | $2$ | $5$ |
152.384.5-152.ba.2.2 | $152$ | $2$ | $2$ | $5$ |
152.384.5-152.bb.1.1 | $152$ | $2$ | $2$ | $5$ |
152.384.5-152.bb.2.2 | $152$ | $2$ | $2$ | $5$ |
304.384.7-304.b.1.3 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.c.1.2 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.k.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.n.1.2 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.w.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.z.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bh.1.1 | $304$ | $2$ | $2$ | $7$ |
304.384.7-304.bi.1.1 | $304$ | $2$ | $2$ | $7$ |