Elliptic curves in class 22.1-c over 4.4.2777.1
Isogeny class 22.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 22.1-c1
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -5 a^{3} + 4 a^{2} + 18 a - 5\) , \( -4 a + 10\bigr] \)
|
| 22.1-c2
| \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + 2 a + 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( 5 a^{3} - 46 a^{2} + 23 a + 25\) , \( -76 a^{3} + 260 a^{2} + 9 a - 124\bigr] \)
|
| 22.1-c3
| \( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( 63 a^{3} - 9 a^{2} - 267 a - 166\) , \( 458 a^{3} - 86 a^{2} - 1890 a - 1084\bigr] \)
|
| 22.1-c4
| \( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( 0\) , \( 4 a^{3} - 4 a^{2} - 4 a\) , \( 15 a^{3} - 18 a^{2} - a + 12\bigr] \)
|
| 22.1-c5
| \( \bigl[a^{2} - 1\) , \( a^{2} - 2 a - 1\) , \( 0\) , \( -a^{3} + a^{2} + a\) , \( 0\bigr] \)
|
| 22.1-c6
| \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a^{3} - 3 a - 1\) , \( 3 a^{3} - 5 a^{2} - 10 a + 8\) , \( 2 a^{3} - 4 a^{2} - 7 a + 6\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 2 & 4 & 2 & 4 \\
2 & 1 & 4 & 8 & 4 & 8 \\
2 & 4 & 1 & 8 & 4 & 8 \\
4 & 8 & 8 & 1 & 2 & 4 \\
2 & 4 & 4 & 2 & 1 & 2 \\
4 & 8 & 8 & 4 & 2 & 1
\end{array}\right)\)
