Elliptic curves in class 29.1-a over 6.6.434581.1
Isogeny class 29.1-a contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 29.1-a1
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 4 a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -34 a^{5} + 81 a^{4} + 65 a^{3} - 117 a^{2} - 27 a + 6\) , \( -56 a^{5} + 163 a^{4} + 31 a^{3} - 264 a^{2} - 13 a + 30\bigr] \)
|
| 29.1-a2
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( -25 a^{5} + 65 a^{4} + 75 a^{3} - 170 a^{2} - 65 a + 5\) , \( -81 a^{5} + 262 a^{4} + 173 a^{3} - 737 a^{2} - 174 a + 41\bigr] \)
|
| 29.1-a3
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - 2 a - 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -29 a^{5} + 67 a^{4} + 95 a^{3} - 175 a^{2} - 56 a + 79\) , \( -60 a^{5} + 141 a^{4} + 189 a^{3} - 364 a^{2} - 105 a + 158\bigr] \)
|
| 29.1-a4
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( 0\) , \( 0\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 5 & 15 \\
3 & 1 & 15 & 5 \\
5 & 15 & 1 & 3 \\
15 & 5 & 3 & 1
\end{array}\right)\)
