Elliptic curves in class 29.2-a over 4.4.2225.1
Isogeny class 29.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 29.2-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( \frac{25}{2} a^{3} + \frac{5}{2} a^{2} - \frac{115}{2} a - 42\) , \( -\frac{31}{2} a^{3} - \frac{3}{2} a^{2} + \frac{155}{2} a + 56\bigr] \)
|
| 29.2-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( 5 a^{3} - 25 a - 17\) , \( 13 a^{3} + 2 a^{2} - 62 a - 45\bigr] \)
|
| 29.2-a3
| \( \bigl[a^{2} - 3\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{3}{2} a + 1\) , \( a + 1\) , \( -3 a^{2} + 4 a + 5\) , \( \frac{7}{2} a^{3} - \frac{21}{2} a^{2} + \frac{1}{2} a + 8\bigr] \)
|
| 29.2-a4
| \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( -a^{2} + 2\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{3}{2} a\) , \( 3 a^{3} - a^{2} - 13 a - 6\) , \( \frac{9}{2} a^{3} + \frac{1}{2} a^{2} - \frac{43}{2} a - 16\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
