Elliptic curves in class 8.2-a over 4.4.2777.1
Isogeny class 8.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
Curve label |
Weierstrass Coefficients |
8.2-a1
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a^{3} - 4 a\) , \( -2 a^{3} - 9 a^{2} - 10 a + 2\) , \( 32 a^{3} + 44 a^{2} - 34 a - 39\bigr] \)
|
8.2-a2
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( -a^{3} - a^{2} + 4 a + 1\bigr] \)
|
8.2-a3
| \( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 2\) , \( 0\) , \( 9 a^{3} - 25 a^{2} + 14 a + 4\) , \( -30 a^{3} + 72 a^{2} + 25 a - 54\bigr] \)
|
8.2-a4
| \( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 2\) , \( 0\) , \( 154 a^{3} - 405 a^{2} + 39 a + 154\) , \( -2510 a^{3} + 6386 a^{2} + 264 a - 3160\bigr] \)
|
8.2-a5
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 3 a^{3} - 2 a^{2} - 9 a - 6\) , \( 6 a^{3} - 3 a^{2} - 22 a - 13\bigr] \)
|
8.2-a6
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 18 a^{3} - 37 a^{2} - 14 a + 4\) , \( 63 a^{3} - 160 a^{2} - 5 a + 73\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 4 & 8 \\
8 & 1 & 4 & 8 & 2 & 4 \\
2 & 4 & 1 & 2 & 2 & 4 \\
4 & 8 & 2 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)