Elliptic curves in class 5.2-b over 4.4.19025.1
Isogeny class 5.2-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 5.2-b1
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 4\) , \( a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 1\) , \( 5 a^{3} + \frac{7}{2} a^{2} - \frac{109}{2} a - 77\) , \( -43 a^{3} - \frac{65}{2} a^{2} + \frac{943}{2} a + 691\bigr] \)
|
| 5.2-b2
| \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 4\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 5\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 4 a\) , \( -\frac{3}{2} a^{3} - 4 a^{2} + \frac{23}{2} a + 29\) , \( -\frac{15}{2} a^{3} - \frac{23}{2} a^{2} + 55 a + 89\bigr] \)
|
| 5.2-b3
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a + 1\) , \( -\frac{35}{2} a^{3} + 60 a^{2} + \frac{289}{2} a - 487\) , \( \frac{411}{2} a^{3} - 794 a^{2} - \frac{2353}{2} a + 4954\bigr] \)
|
| 5.2-b4
| \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a + 1\) , \( -5 a^{3} + \frac{35}{2} a^{2} + \frac{69}{2} a - 122\) , \( -\frac{33}{2} a^{3} + 61 a^{2} + \frac{219}{2} a - 422\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
