Elliptic curves in class 12.1-a over 4.4.17428.1
Isogeny class 12.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 12.1-a1
| \( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( a^{3} - 4 a - 2\) , \( a^{3} - 4 a\) , \( 10 a^{3} + 16 a^{2} - 31 a - 27\) , \( -41 a^{3} - 56 a^{2} + 113 a + 102\bigr] \)
|
| 12.1-a2
| \( \bigl[a^{2} - 2\) , \( -a^{3} + 5 a + 1\) , \( a^{3} + a^{2} - 3 a - 4\) , \( 17 a^{3} - 62 a^{2} + 20 a + 63\) , \( -146 a^{3} + 446 a^{2} - 72 a - 406\bigr] \)
|
| 12.1-a3
| \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -5 a^{3} + 5 a^{2} + 22 a - 22\) , \( -9 a^{3} + 15 a^{2} + 40 a - 67\bigr] \)
|
| 12.1-a4
| \( \bigl[a\) , \( a^{3} - 5 a - 1\) , \( a\) , \( -12 a^{3} + 17 a^{2} + 62 a - 86\) , \( -60 a^{3} + 104 a^{2} + 291 a - 477\bigr] \)
|
| 12.1-a5
| \( \bigl[a\) , \( a^{3} - 4 a - 1\) , \( 0\) , \( 24 a^{3} - 81 a^{2} + 25 a + 82\) , \( 2364 a^{3} - 7244 a^{2} + 1134 a + 6543\bigr] \)
|
| 12.1-a6
| \( \bigl[a\) , \( -a^{2} - a + 2\) , \( 0\) , \( 20 a^{3} + 20 a^{2} - 70 a - 56\) , \( 62 a^{3} + 71 a^{2} - 204 a - 174\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 4 & 8 & 8 \\
4 & 1 & 2 & 4 & 8 & 8 \\
2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 2 & 1 & 2 & 2 \\
8 & 8 & 4 & 2 & 1 & 4 \\
8 & 8 & 4 & 2 & 4 & 1
\end{array}\right)\)
