Elliptic curves in class 6.1-a over 4.4.13068.1
Isogeny class 6.1-a contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 6.1-a1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 129 a^{3} - 109 a^{2} - 753 a - 373\) , \( 1326 a^{3} - 994 a^{2} - 8022 a - 3893\bigr] \)
|
| 6.1-a2
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -41 a^{3} + 21 a^{2} + 137 a - 83\) , \( -266 a^{3} - 66 a^{2} + 602 a - 309\bigr] \)
|
| 6.1-a3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( 4 a^{3} - 4 a^{2} - 28 a - 28\) , \( 20 a^{3} - 20 a^{2} - 140 a - 79\bigr] \)
|
| 6.1-a4
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a\) , \( -a^{3} + 2 a^{2} + 4 a - 2\) , \( -a^{3} + a^{2} + 7 a - 3\) , \( -3\bigr] \)
|
| 6.1-a5
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 1\) , \( a^{2} - a - 3\) , \( 4 a^{3} - 4 a^{2} - 28 a + 9\) , \( 23 a^{3} - 23 a^{2} - 161 a + 52\bigr] \)
|
| 6.1-a6
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a + 1\) , \( 28 a^{3} - 83 a^{2} - 13 a + 22\) , \( -194 a^{3} + 546 a^{2} + 168 a - 104\bigr] \)
|
| 6.1-a7
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 5 a + 1\) , \( a + 1\) , \( 463 a^{3} - 1313 a^{2} - 378 a + 262\) , \( -13942 a^{3} + 39369 a^{2} + 11842 a - 7637\bigr] \)
|
| 6.1-a8
| \( \bigl[a\) , \( -2 a^{3} + 3 a^{2} + 11 a\) , \( a^{2} - 2 a - 3\) , \( a^{3} - 3 a + 7\) , \( -5 a^{3} - 5 a^{2} + 7 a - 4\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 2 & 4 & 16 & 8 & 16 & 8 \\
4 & 1 & 2 & 4 & 16 & 8 & 16 & 8 \\
2 & 2 & 1 & 2 & 8 & 4 & 8 & 4 \\
4 & 4 & 2 & 1 & 4 & 2 & 4 & 2 \\
16 & 16 & 8 & 4 & 1 & 2 & 4 & 8 \\
8 & 8 & 4 & 2 & 2 & 1 & 2 & 4 \\
16 & 16 & 8 & 4 & 4 & 2 & 1 & 8 \\
8 & 8 & 4 & 2 & 8 & 4 & 8 & 1
\end{array}\right)\)
