Elliptic curves in class 20.2-c over 4.4.19025.1
Isogeny class 20.2-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 20.2-c1
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( 1\) , \( 23 a^{3} - \frac{27}{2} a^{2} - \frac{763}{2} a - 501\) , \( -495 a^{3} - 1369 a^{2} + 1099 a + 3448\bigr] \)
|
| 20.2-c2
| \( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( 1\) , \( -\frac{79}{2} a^{3} - \frac{137}{2} a^{2} + 261 a + 454\) , \( -940 a^{3} - 1459 a^{2} + 7016 a + 11670\bigr] \)
|
| 20.2-c3
| \( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( -25 a^{3} + \frac{181}{2} a^{2} + \frac{325}{2} a - 600\) , \( -205 a^{3} + 763 a^{2} + 1332 a - 5151\bigr] \)
|
| 20.2-c4
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 3\) , \( 0\) , \( -386 a^{3} + 1435 a^{2} + 2509 a - 9706\) , \( -\frac{27673}{2} a^{3} + 51572 a^{2} + \frac{179841}{2} a - 348886\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 1\)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
