Elliptic curves in class 5.2-a over 4.4.19025.1
Isogeny class 5.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 5.2-a1
| \( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( 0\) , \( a\) , \( \frac{55}{2} a^{3} + 19 a^{2} - \frac{609}{2} a - 440\) , \( \frac{665}{2} a^{3} + \frac{487}{2} a^{2} - 3658 a - 5350\bigr] \)
|
| 5.2-a2
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -\frac{29}{2} a^{3} - 3 a^{2} + \frac{205}{2} a + 39\) , \( \frac{153}{2} a^{3} + \frac{75}{2} a^{2} - 550 a - 356\bigr] \)
|
| 5.2-a3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a\) , \( 1\) , \( -5 a^{3} + 18 a^{2} + 29 a - 104\) , \( 12 a^{3} - \frac{85}{2} a^{2} - \frac{197}{2} a + 346\bigr] \)
|
| 5.2-a4
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a\) , \( 1\) , \( -2 a^{2} + 4 a + 11\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 8\bigr] \)
|
| 5.2-a5
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a + 1\) , \( \frac{1}{2} a^{3} - a^{2} - \frac{9}{2} a + 4\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a^{2} - 5 a + 46\) , \( \frac{1}{2} a^{3} - \frac{67}{2} a^{2} + 50 a + 223\bigr] \)
|
| 5.2-a6
| \( \bigl[1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{9}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -32 a^{3} - \frac{35}{2} a^{2} + \frac{463}{2} a + 165\) , \( 800 a^{3} - 1676 a^{2} - 5408 a + 10941\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 4 & 2 & 8 & 8 \\
4 & 1 & 4 & 2 & 2 & 2 \\
4 & 4 & 1 & 2 & 8 & 8 \\
2 & 2 & 2 & 1 & 4 & 4 \\
8 & 2 & 8 & 4 & 1 & 4 \\
8 & 2 & 8 & 4 & 4 & 1
\end{array}\right)\)
