Elliptic curves in class 8.2-b over 4.4.11348.1
Isogeny class 8.2-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 8.2-b1
| \( \bigl[a^{3} - 4 a - 3\) , \( a^{2} - 4\) , \( a + 1\) , \( -11 a^{3} + 30 a^{2} + 6 a - 5\) , \( 7 a^{3} - 17 a^{2} + 2 a + 7\bigr] \)
|
| 8.2-b2
| \( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -654 a^{3} + 1043 a^{2} + 2660 a - 2235\) , \( -14751 a^{3} + 23453 a^{2} + 59929 a - 50085\bigr] \)
|
| 8.2-b3
| \( \bigl[a^{3} - 4 a - 3\) , \( a^{3} - 5 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -39 a^{3} + 63 a^{2} + 165 a - 140\) , \( -236 a^{3} + 379 a^{2} + 958 a - 803\bigr] \)
|
| 8.2-b4
| \( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a + 1\) , \( 137 a^{3} - 39 a^{2} - 713 a - 378\) , \( 2176 a^{3} - 601 a^{2} - 11316 a - 6015\bigr] \)
|
| 8.2-b5
| \( \bigl[a^{2} - 3\) , \( -a^{3} + a^{2} + 5 a\) , \( a + 1\) , \( 5 a^{3} - 11 a^{2} - 19 a + 29\) , \( 12 a^{3} - 23 a^{2} - 51 a + 49\bigr] \)
|
| 8.2-b6
| \( \bigl[a^{2} - 3\) , \( -a^{2} + 4\) , \( a^{2} - 3\) , \( -2 a^{2} + 6\) , \( -a^{2} + 3\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 4 & 2 \\
8 & 1 & 2 & 4 & 8 & 4 \\
4 & 2 & 1 & 2 & 4 & 2 \\
8 & 4 & 2 & 1 & 8 & 4 \\
4 & 8 & 4 & 8 & 1 & 2 \\
2 & 4 & 2 & 4 & 2 & 1
\end{array}\right)\)
