Elliptic curves in class 8.4-b over 4.4.9248.1
Isogeny class 8.4-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 8.4-b1
| \( \bigl[a^{2} - 3\) , \( -1\) , \( a^{2} - 3\) , \( a^{2} - 6\) , \( 6 a^{2} - 28\bigr] \)
|
| 8.4-b2
| \( \bigl[a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{2} - 3\) , \( 14 a^{3} - 9 a^{2} - 63 a + 44\) , \( 30 a^{3} - 19 a^{2} - 136 a + 88\bigr] \)
|
| 8.4-b3
| \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( -7 a^{3} - 12 a^{2} + 13 a + 12\) , \( 13 a^{3} + 28 a^{2} - 5 a - 12\bigr] \)
|
| 8.4-b4
| \( \bigl[a + 1\) , \( a^{3} - a^{2} - 5 a + 3\) , \( a^{3} + a^{2} - 3 a - 3\) , \( 65 a^{3} - 147 a^{2} - 27 a + 67\) , \( -888 a^{3} + 1906 a^{2} + 386 a - 838\bigr] \)
|
| 8.4-b5
| \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 3 a\) , \( -195 a^{3} + 125 a^{2} + 888 a - 572\) , \( -2474 a^{3} + 1636 a^{2} + 11286 a - 7467\bigr] \)
|
| 8.4-b6
| \( \bigl[a + 1\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 3 a\) , \( -15 a^{3} + 5 a^{2} + 68 a - 27\) , \( -44 a^{3} + 26 a^{2} + 201 a - 122\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 8 & 4 & 2 \\
8 & 1 & 2 & 4 & 8 & 4 \\
4 & 2 & 1 & 2 & 4 & 2 \\
8 & 4 & 2 & 1 & 8 & 4 \\
4 & 8 & 4 & 8 & 1 & 2 \\
2 & 4 & 2 & 4 & 2 & 1
\end{array}\right)\)
