Isogeny class 20.3-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 20.3-a1
| \( \bigl[\frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{13}{8} a - \frac{7}{2}\) , \( -\frac{1}{8} a^{3} + \frac{1}{2} a^{2} + \frac{13}{8} a - \frac{5}{2}\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{3}{2}\) , \( -\frac{1}{2} a^{3} + \frac{9}{2} a + 8\) , \( \frac{1}{8} a^{3} + a^{2} - \frac{25}{8} a - \frac{13}{2}\bigr] \)
|
| 20.3-a2
| \( \bigl[-\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{1}{2}\) , \( -1\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{13}{8} a - \frac{5}{2}\) , \( -\frac{183}{8} a^{3} + 28 a^{2} + \frac{2119}{8} a - \frac{651}{2}\) , \( -\frac{845}{4} a^{3} + \frac{493}{2} a^{2} + \frac{9823}{4} a - 2868\bigr] \)
|
| 20.3-a3
| \( \bigl[1\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 3\) , \( 0\) , \( \frac{489}{8} a^{3} + 74 a^{2} - \frac{5705}{8} a - \frac{1699}{2}\) , \( 1012 a^{3} + \frac{2371}{2} a^{2} - \frac{23521}{2} a - 13788\bigr] \)
|
| 20.3-a4
| \( \bigl[1\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{1}{2}\) , \( \frac{1}{8} a^{3} + \frac{1}{2} a^{2} - \frac{13}{8} a - \frac{5}{2}\) , \( 2 a^{3} + 2 a^{2} - 24 a - 27\) , \( -\frac{33}{8} a^{3} - \frac{11}{2} a^{2} + \frac{373}{8} a + \frac{111}{2}\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
