Elliptic curves in class 20.2-a over 4.4.12400.1
Isogeny class 20.2-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 20.2-a1
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{9}{2} a + \frac{9}{2}\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a\) , \( \frac{25}{2} a^{3} - 31 a^{2} - \frac{213}{2} a + 227\) , \( 100 a^{3} - \frac{385}{2} a^{2} - 824 a + \frac{3181}{2}\bigr] \)
|
| 20.2-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + a + \frac{9}{2}\) , \( 1\) , \( -\frac{535}{2} a^{3} - \frac{1509}{2} a^{2} + \frac{2047}{2} a + \frac{5661}{2}\) , \( 7835 a^{3} + \frac{44931}{2} a^{2} - 29505 a - \frac{169025}{2}\bigr] \)
|
| 20.2-a3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{7}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{2} + a + \frac{9}{2}\) , \( 1\) , \( -\frac{615}{2} a^{3} - \frac{1389}{2} a^{2} + \frac{2667}{2} a + \frac{4561}{2}\) , \( 7893 a^{3} + \frac{41839}{2} a^{2} - 31319 a - \frac{151229}{2}\bigr] \)
|
| 20.2-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a\) , \( \frac{1}{2} a^{2} + a - \frac{7}{2}\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{7}{2}\) , \( -\frac{883}{2} a^{3} + \frac{1699}{2} a^{2} + \frac{7273}{2} a - \frac{14081}{2}\) , \( \frac{21077}{2} a^{3} - 20505 a^{2} - \frac{173719}{2} a + 168747\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
