Invariants
Level: | $152$ | $\SL_2$-level: | $8$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (of which $2$ are rational) | Cusp widths | $4^{8}\cdot8^{2}$ | Cusp orbits | $1^{2}\cdot2^{2}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $2$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 8N0 |
Level structure
$\GL_2(\Z/152\Z)$-generators: | $\begin{bmatrix}55&0\\150&59\end{bmatrix}$, $\begin{bmatrix}55&40\\124&145\end{bmatrix}$, $\begin{bmatrix}97&104\\22&31\end{bmatrix}$, $\begin{bmatrix}127&20\\92&3\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 152.48.0.i.2 for the level structure with $-I$) |
Cyclic 152-isogeny field degree: | $40$ |
Cyclic 152-torsion field degree: | $2880$ |
Full 152-torsion field degree: | $1969920$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has infinitely many rational points but none with conductor small enough to be contained within the database of elliptic curves over $\Q$.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.e.1.15 | $8$ | $2$ | $2$ | $0$ | $0$ |
152.48.0-8.e.1.2 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.48.0-76.c.1.1 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.48.0-76.c.1.13 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.48.0-152.h.1.12 | $152$ | $2$ | $2$ | $0$ | $?$ |
152.48.0-152.h.1.30 | $152$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
152.192.1-152.i.1.8 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.y.1.2 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.bc.1.4 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.bg.1.6 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.bu.1.6 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.by.1.4 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.cb.1.2 | $152$ | $2$ | $2$ | $1$ |
152.192.1-152.cd.1.8 | $152$ | $2$ | $2$ | $1$ |