Elliptic curves in class 6.1-c over 4.4.16609.1
Isogeny class 6.1-c contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 6.1-c1
| \( \bigl[a^{2} - 4\) , \( -a^{2} + a + 3\) , \( a + 1\) , \( 8 a^{3} + 11 a^{2} - 47 a - 68\) , \( 43 a^{3} + 50 a^{2} - 241 a - 326\bigr] \)
|
| 6.1-c2
| \( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 3 a - 1\) , \( 22 a^{3} - 22 a^{2} - 68 a + 19\) , \( 18 a^{3} - 58 a^{2} - 7 a + 173\bigr] \)
|
| 6.1-c3
| \( \bigl[a^{3} - 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 3 a - 1\) , \( 192 a^{3} - 387 a^{2} - 483 a + 739\) , \( 3037 a^{3} - 6509 a^{2} - 7385 a + 12917\bigr] \)
|
| 6.1-c4
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - 2 a^{2} - 5 a + 7\) , \( 0\) , \( -a^{3} + 2 a^{2} + 5 a - 8\) , \( 0\bigr] \)
|
| 6.1-c5
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - 2 a^{2} - 5 a + 7\) , \( 0\) , \( 4 a^{3} - 8 a^{2} - 20 a + 32\) , \( 38 a^{3} - 61 a^{2} - 186 a + 251\bigr] \)
|
| 6.1-c6
| \( \bigl[1\) , \( -a^{2} - a + 3\) , \( 0\) , \( -a^{3} + 5 a^{2} + 4 a - 14\) , \( a^{3} - 2 a + 3\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 8 & 2 & 4 & 8 \\
4 & 1 & 2 & 2 & 4 & 2 \\
8 & 2 & 1 & 4 & 8 & 4 \\
2 & 2 & 4 & 1 & 2 & 4 \\
4 & 4 & 8 & 2 & 1 & 8 \\
8 & 2 & 4 & 4 & 8 & 1
\end{array}\right)\)
