Elliptic curves in class 20.2-a over 4.4.19025.1
Isogeny class 20.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 20.2-a1
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -66 a^{3} + 240 a^{2} + 430 a - 1621\) , \( -\frac{1695}{2} a^{3} + \frac{6233}{2} a^{2} + 5515 a - 21072\bigr] \)
|
| 20.2-a2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -\frac{7}{2} a^{3} + 15 a^{2} + \frac{45}{2} a - 101\) , \( -\frac{19}{2} a^{3} + \frac{75}{2} a^{2} + 62 a - 256\bigr] \)
|
| 20.2-a3
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 5 a\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( -\frac{3}{2} a^{3} + a^{2} + \frac{25}{2} a + 14\) , \( -a^{3} + a^{2} + 9 a + 7\bigr] \)
|
| 20.2-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a - 1\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{19}{2} a^{3} - 49 a^{2} + \frac{13}{2} a + 210\) , \( -49 a^{3} + 346 a^{2} - 152 a - 1569\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
