Elliptic curves in class 29.1-a over 4.4.2225.1
Isogeny class 29.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
Curve label |
Weierstrass Coefficients |
29.1-a1
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -\frac{1}{2} a^{3} + \frac{3}{2} a^{2} + \frac{3}{2} a - 2\) , \( a^{2} - 3\) , \( \frac{1}{2} a^{3} + \frac{5}{2} a^{2} + \frac{1}{2} a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} + \frac{1}{2} a - 1\bigr] \)
|
29.1-a2
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( -a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{1}{2} a\) , \( \frac{3}{2} a^{3} - \frac{1}{2} a^{2} - \frac{17}{2} a - 4\) , \( 6 a^{3} - 29 a - 20\bigr] \)
|
29.1-a3
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( 3 a^{3} - 6 a^{2} - 3 a - 1\) , \( \frac{19}{2} a^{3} - \frac{47}{2} a^{2} - \frac{15}{2} a + 20\bigr] \)
|
29.1-a4
| \( \bigl[\frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 2\) , \( a^{2} - a - 3\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - 3\) , \( \frac{21}{2} a^{3} - \frac{47}{2} a^{2} - \frac{31}{2} a + 24\) , \( -8 a^{3} + 26 a^{2} - 9 a - 17\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)