Elliptic curves in class 10.1-b over 4.4.6809.1
Isogeny class 10.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 10.1-b1
| \( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 0\) , \( a^{3} - 4 a^{2} - 3 a + 18\) , \( 788 a^{3} - 463 a^{2} - 3672 a + 1371\bigr] \)
|
| 10.1-b2
| \( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 1\) , \( -3 a^{3} - 4 a^{2} + 2 a - 5\) , \( -a^{3} + 5 a^{2} + 22 a + 15\bigr] \)
|
| 10.1-b3
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( -38 a^{3} + 22 a^{2} + 176 a - 67\) , \( -190 a^{3} + 111 a^{2} + 884 a - 330\bigr] \)
|
| 10.1-b4
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 142 a^{3} - 83 a^{2} - 659 a + 233\) , \( -538 a^{3} + 311 a^{2} + 2511 a - 925\bigr] \)
|
| 10.1-b5
| \( \bigl[a\) , \( a^{2} - 3\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a^{2} + a - 2\bigr] \)
|
| 10.1-b6
| \( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 5\) , \( a^{2} - 2\) , \( -41 a^{3} + 24 a^{2} + 203 a - 101\) , \( -259 a^{3} + 953 a^{2} - 858 a + 75\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 8 & 4 \\
2 & 1 & 2 & 4 & 4 & 2 \\
4 & 2 & 1 & 2 & 2 & 4 \\
8 & 4 & 2 & 1 & 4 & 8 \\
8 & 4 & 2 & 4 & 1 & 8 \\
4 & 2 & 4 & 8 & 8 & 1
\end{array}\right)\)
