Elliptic curves in class 22.1-b over 4.4.2777.1
Isogeny class 22.1-b contains
8 curves linked by isogenies of
degrees dividing 20.
| Curve label |
Weierstrass Coefficients |
| 22.1-b1
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - 2\) , \( 574 a^{3} - 1057 a^{2} - 549 a - 385\) , \( 14427 a^{3} - 29786 a^{2} - 11937 a + 4219\bigr] \)
|
| 22.1-b2
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - 2\) , \( 9 a^{3} + 8 a^{2} - 59 a - 35\) , \( -37 a^{3} + 17 a^{2} + 136 a + 71\bigr] \)
|
| 22.1-b3
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{2} - 2\) , \( 4 a^{3} - 7 a^{2} - 9 a + 5\) , \( -a^{3} + 2 a^{2} + a - 3\bigr] \)
|
| 22.1-b4
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -25 a^{3} + 26 a^{2} + 84 a - 75\) , \( -255 a^{3} - 134 a^{2} + 413 a - 111\bigr] \)
|
| 22.1-b5
| \( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a - 1\) , \( -2 a - 2\) , \( 28 a^{3} - 47 a^{2} - 81 a + 81\bigr] \)
|
| 22.1-b6
| \( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - 2 a - 3\) , \( a^{2} - a - 1\) , \( -833 a^{3} - 1088 a^{2} + 652 a + 590\) , \( -39688 a^{3} - 53892 a^{2} + 31054 a + 33219\bigr] \)
|
| 22.1-b7
| \( \bigl[a^{2} - a - 1\) , \( a^{3} - 4 a - 2\) , \( 0\) , \( 4 a^{3} - 15 a^{2} + 7 a + 9\) , \( 26 a^{3} - 63 a^{2} - 10 a + 33\bigr] \)
|
| 22.1-b8
| \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a\) , \( -506 a^{3} - 392 a^{2} + 539 a - 67\) , \( -15172 a^{3} - 18204 a^{2} + 13108 a + 9055\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrrrrrr}
1 & 5 & 10 & 4 & 20 & 2 & 20 & 4 \\
5 & 1 & 2 & 20 & 4 & 10 & 4 & 20 \\
10 & 2 & 1 & 10 & 2 & 5 & 2 & 10 \\
4 & 20 & 10 & 1 & 5 & 2 & 20 & 4 \\
20 & 4 & 2 & 5 & 1 & 10 & 4 & 20 \\
2 & 10 & 5 & 2 & 10 & 1 & 10 & 2 \\
20 & 4 & 2 & 20 & 4 & 10 & 1 & 5 \\
4 & 20 & 10 & 4 & 20 & 2 & 5 & 1
\end{array}\right)\)
