Elliptic curves in class 47.1-c over 4.4.4913.1
Isogeny class 47.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 47.1-c1
| \( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( 2 a^{3} - 4 a^{2} + 12 a\) , \( -\frac{7}{2} a^{3} + 20 a^{2} + 4 a - \frac{7}{2}\bigr] \)
|
| 47.1-c2
| \( \bigl[a^{2} - 2\) , \( a^{2} - 2 a - 4\) , \( a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a + \frac{5}{2}\) , \( -a^{3} + 4 a + 1\bigr] \)
|
| 47.1-c3
| \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( 0\) , \( -\frac{3}{2} a^{3} + 2 a^{2} + 8 a - \frac{7}{2}\) , \( 0\bigr] \)
|
| 47.1-c4
| \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + a^{2} + 2 a - \frac{3}{2}\) , \( 0\) , \( 6 a^{3} - 8 a^{2} - 32 a + 14\) , \( -\frac{17}{2} a^{3} + 11 a^{2} + 51 a - \frac{63}{2}\bigr] \)
|
| 47.1-c5
| \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( 1\) , \( \frac{1}{2} a^{3} - 3 a - \frac{1}{2}\) , \( \frac{3}{2} a^{3} - a^{2} - 9 a - \frac{9}{2}\) , \( -a^{3} + a^{2} + 5 a - 1\bigr] \)
|
| 47.1-c6
| \( \bigl[\frac{1}{2} a^{3} - 2 a - \frac{3}{2}\) , \( a^{2} - 3\) , \( a^{2} - a - 2\) , \( -2 a^{3} + 7 a^{2} + 7 a - 7\) , \( 3 a^{3} + 2 a^{2} - 27 a + 11\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 2 & 4 & 2 \\
8 & 4 & 2 & 1 & 8 & 4 \\
4 & 2 & 4 & 8 & 1 & 8 \\
8 & 4 & 2 & 4 & 8 & 1
\end{array}\right)\)
