Elliptic curves in class 32.2-b over 6.6.1868969.1
Isogeny class 32.2-b contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 32.2-b1
| \( \bigl[a^{5} - 5 a^{3} + 5 a - 2\) , \( -a^{5} + 4 a^{3} + a^{2} - 2 a\) , \( a^{5} - 5 a^{3} - a^{2} + 5 a\) , \( a^{4} - 6 a^{2} - 3 a + 3\) , \( 10 a^{5} + 12 a^{4} - 46 a^{3} - 67 a^{2} + 3 a + 19\bigr] \)
|
| 32.2-b2
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 4\) , \( -2 a^{4} + a^{3} + 9 a^{2} - a - 5\) , \( a^{5} - 4 a^{3} - a^{2} + 2 a\) , \( 23 a^{5} + 22 a^{4} - 106 a^{3} - 128 a^{2} + 16 a + 30\) , \( 161 a^{5} + 185 a^{4} - 754 a^{3} - 1026 a^{2} + 110 a + 284\bigr] \)
|
| 32.2-b3
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 4\) , \( -2 a^{4} + a^{3} + 9 a^{2} - a - 5\) , \( a^{5} - 4 a^{3} - a^{2} + 2 a\) , \( 28 a^{5} + 22 a^{4} - 121 a^{3} - 118 a^{2} - 14 a - 45\) , \( 81 a^{5} + 97 a^{4} - 437 a^{3} - 589 a^{2} + 308 a + 447\bigr] \)
|
| 32.2-b4
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 4 a^{2} + 2 a - 4\) , \( -2 a^{4} + a^{3} + 9 a^{2} - a - 5\) , \( a^{5} - 4 a^{3} - a^{2} + 2 a\) , \( 353 a^{5} + 412 a^{4} - 1641 a^{3} - 2293 a^{2} + 216 a + 620\) , \( 8440 a^{5} + 9759 a^{4} - 39457 a^{3} - 53946 a^{2} + 5390 a + 14656\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
