$\GL_2(\Z/40\Z)$-generators: |
$\begin{bmatrix}5&2\\38&15\end{bmatrix}$, $\begin{bmatrix}17&36\\14&25\end{bmatrix}$, $\begin{bmatrix}19&0\\34&23\end{bmatrix}$, $\begin{bmatrix}37&28\\5&37\end{bmatrix}$ |
Contains $-I$: |
yes |
Quadratic refinements: |
40.24.0-40.p.1.1, 40.24.0-40.p.1.2, 40.24.0-40.p.1.3, 40.24.0-40.p.1.4, 80.24.0-40.p.1.1, 80.24.0-40.p.1.2, 80.24.0-40.p.1.3, 80.24.0-40.p.1.4, 120.24.0-40.p.1.1, 120.24.0-40.p.1.2, 120.24.0-40.p.1.3, 120.24.0-40.p.1.4, 240.24.0-40.p.1.1, 240.24.0-40.p.1.2, 240.24.0-40.p.1.3, 240.24.0-40.p.1.4, 280.24.0-40.p.1.1, 280.24.0-40.p.1.2, 280.24.0-40.p.1.3, 280.24.0-40.p.1.4 |
Cyclic 40-isogeny field degree: |
$24$ |
Cyclic 40-torsion field degree: |
$384$ |
Full 40-torsion field degree: |
$61440$ |
This modular curve is isomorphic to $\mathbb{P}^1$.
This modular curve has infinitely many rational points, including 28 stored non-cuspidal points.
Maps to other modular curves
$j$-invariant map
of degree 12 to the modular curve
$X(1)$
:
$\displaystyle j$ |
$=$ |
$\displaystyle \frac{2^5}{3^4\cdot5}\cdot\frac{(8x+y)^{12}(31744x^{4}+20480x^{3}y+18240x^{2}y^{2}+3200xy^{3}+775y^{4})^{3}}{(8x+y)^{12}(32x^{2}-5y^{2})^{4}(32x^{2}+8xy+5y^{2})^{2}}$ |
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Cover information
Click on a modular curve in the diagram to see information about it.
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This modular curve minimally covers the modular curves listed below.
This modular curve is minimally covered by the modular curves in the database listed below.