Elliptic curves in class 32.2-c over 6.6.1868969.1
Isogeny class 32.2-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 32.2-c1
| \( \bigl[a^{5} + a^{4} - 5 a^{3} - 6 a^{2} + 4 a + 4\) , \( -a^{5} - a^{4} + 6 a^{3} + 5 a^{2} - 5 a - 1\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 2\) , \( -a^{5} - 3 a^{4} + 6 a^{3} + 13 a^{2} + 2 a\) , \( a^{5} - 6 a^{4} - 3 a^{3} + 27 a^{2} + 4 a - 8\bigr] \)
|
| 32.2-c2
| \( \bigl[a^{5} - 4 a^{3} - a^{2} + 2 a\) , \( -a^{5} + 4 a^{3} + 2 a^{2} - a\) , \( a^{5} - 4 a^{3} - a^{2} + a\) , \( 99 a^{5} + 120 a^{4} - 460 a^{3} - 649 a^{2} + 49 a + 169\) , \( -948 a^{5} - 1086 a^{4} + 4434 a^{3} + 6036 a^{2} - 626 a - 1651\bigr] \)
|
| 32.2-c3
| \( \bigl[a^{5} - 4 a^{3} - a^{2} + 2 a\) , \( -a^{5} + 4 a^{3} + 2 a^{2} - a\) , \( a^{5} - 4 a^{3} - a^{2} + a\) , \( 119 a^{5} + 165 a^{4} - 515 a^{3} - 859 a^{2} - 131 a + 114\) , \( 431 a^{5} + 647 a^{4} - 1768 a^{3} - 3318 a^{2} - 949 a + 225\bigr] \)
|
| 32.2-c4
| \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 8\) , \( a^{5} - 5 a^{3} + 5 a - 2\) , \( -8 a^{5} + 207 a^{4} + a^{3} - 931 a^{2} - 80 a + 281\) , \( 57 a^{5} - 2198 a^{4} + 51 a^{3} + 9793 a^{2} + 1325 a - 2936\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
