Elliptic curves in class 12.1-a over 4.4.13068.1
Isogeny class 12.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-a1
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( -1\) , \( a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 7 a + 2\) , \( -3 a^{3} + 3 a^{2} + 21 a - 9\bigr] \)
|
| 12.1-a2
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a\) , \( 0\) , \( 18 a^{3} - 18 a^{2} - 126 a - 47\) , \( -69 a^{3} + 69 a^{2} + 483 a + 243\bigr] \)
|
| 12.1-a3
| \( \bigl[-a^{3} + 2 a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 7 a\) , \( 0\) , \( 3 a^{3} - 3 a^{2} - 21 a + 3\) , \( 9\bigr] \)
|
| 12.1-a4
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 2\) , \( 13 a^{3} - 36 a^{2} - 13 a + 9\) , \( 48 a^{3} - 135 a^{2} - 43 a + 24\bigr] \)
|
| 12.1-a5
| \( \bigl[a^{3} - a^{2} - 6 a - 1\) , \( -a^{3} + a^{2} + 7 a\) , \( a^{2} - a - 2\) , \( 208 a^{3} - 571 a^{2} - 218 a + 89\) , \( 3802 a^{3} - 10670 a^{2} - 3396 a + 1971\bigr] \)
|
| 12.1-a6
| \( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 9 a + 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( 3 a^{3} + 3 a^{2} - 3 a + 6\) , \( 25 a^{3} + 52 a^{2} + 10 a - 4\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 4 & 8 \\
8 & 1 & 2 & 4 & 8 & 4 \\
4 & 2 & 1 & 2 & 4 & 2 \\
2 & 4 & 2 & 1 & 2 & 4 \\
4 & 8 & 4 & 2 & 1 & 8 \\
8 & 4 & 2 & 4 & 8 & 1
\end{array}\right)\)
