↑

Properties

Label 276.48.0.c.1
Level $276$
Index $48$
Genus $0$
Cusps $10$
$\Q$-cusps $2$

Related objects

Downloads

Learn more

Invariants

Level: $276$ $\SL_2$-level: $12$
Index: $48$ $\PSL_2$-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 $1^{2}\cdot2\cdot3^{2}\cdot4^{2}\cdot6\cdot12^{2}$ Cusp orbits $1^{2}\cdot2^{4}$
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: 12J0

Level structure

$\GL_2(\Z/276\Z)$-generators: $\begin{bmatrix}0&131\\227&0\end{bmatrix}$, $\begin{bmatrix}15&32\\86&189\end{bmatrix}$, $\begin{bmatrix}63&214\\164&181\end{bmatrix}$, $\begin{bmatrix}182&87\\167&106\end{bmatrix}$, $\begin{bmatrix}193&210\\70&5\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 276.96.0-276.c.1.1, 276.96.0-276.c.1.2, 276.96.0-276.c.1.3, 276.96.0-276.c.1.4, 276.96.0-276.c.1.5, 276.96.0-276.c.1.6, 276.96.0-276.c.1.7, 276.96.0-276.c.1.8, 276.96.0-276.c.1.9, 276.96.0-276.c.1.10, 276.96.0-276.c.1.11, 276.96.0-276.c.1.12, 276.96.0-276.c.1.13, 276.96.0-276.c.1.14, 276.96.0-276.c.1.15, 276.96.0-276.c.1.16
Cyclic 276-isogeny field degree: $24$
Cyclic 276-torsion field degree: $2112$
Full 276-torsion field degree: $25648128$

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
$X_0(12)$ $12$ $2$ $2$ $0$ $0$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus
276.96.1.b.3 $276$ $2$ $2$ $1$
276.96.1.i.2 $276$ $2$ $2$ $1$
276.96.1.j.1 $276$ $2$ $2$ $1$
276.96.1.k.1 $276$ $2$ $2$ $1$
276.96.1.l.1 $276$ $2$ $2$ $1$
276.96.1.m.1 $276$ $2$ $2$ $1$
276.96.1.n.2 $276$ $2$ $2$ $1$
276.96.1.o.4 $276$ $2$ $2$ $1$
276.144.3.c.1 $276$ $3$ $3$ $3$