Elliptic curves in class 8.1-a over 4.4.13068.1
Isogeny class 8.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 8.1-a1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 0\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 5 a^{3} - 5 a^{2} - 35 a - 12\) , \( -7 a^{3} + 7 a^{2} + 49 a + 24\bigr] \)
|
| 8.1-a2
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( 0\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -3 a^{3} + 3 a^{2} + 21 a - 8\) , \( -11 a^{3} + 11 a^{2} + 77 a - 28\bigr] \)
|
| 8.1-a3
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 26 a^{3} - 78 a^{2} - 10 a + 21\) , \( -111 a^{3} + 309 a^{2} + 105 a - 54\bigr] \)
|
| 8.1-a4
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 320 a^{3} - 908 a^{2} - 260 a + 181\) , \( 6179 a^{3} - 17453 a^{2} - 5237 a + 3392\bigr] \)
|
| 8.1-a5
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 6 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1790 a^{3} - 5058 a^{2} - 1510 a + 981\) , \( -101387 a^{3} + 286329 a^{2} + 86037 a - 55592\bigr] \)
|
| 8.1-a6
| \( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -45 a^{3} - 42 a^{2} + 31 a - 78\) , \( -446 a^{3} - 1388 a^{2} - 938 a + 200\bigr] \)
|
| 8.1-a7
| \( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -5 a^{3} - 12 a^{2} - 9 a - 8\) , \( 18 a^{3} + 36 a^{2} + 6 a\bigr] \)
|
| 8.1-a8
| \( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 3 a^{3} - 6 a^{2} - 17 a + 6\) , \( -6 a^{3} + 4 a^{2} + 22 a - 10\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 4 & 6 & 12 & 4 & 2 & 3 \\
12 & 1 & 3 & 2 & 4 & 12 & 6 & 4 \\
4 & 3 & 1 & 6 & 12 & 4 & 2 & 12 \\
6 & 2 & 6 & 1 & 2 & 6 & 3 & 2 \\
12 & 4 & 12 & 2 & 1 & 3 & 6 & 4 \\
4 & 12 & 4 & 6 & 3 & 1 & 2 & 12 \\
2 & 6 & 2 & 3 & 6 & 2 & 1 & 6 \\
3 & 4 & 12 & 2 & 4 & 12 & 6 & 1
\end{array}\right)\)
