Elliptic curves in class 16.2-a over 4.4.9248.1
Isogeny class 16.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 16.2-a1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{3} - a^{2} - 5 a + 2\) , \( a\) , \( 3441 a^{3} + 2276 a^{2} - 15696 a - 10385\) , \( -180088 a^{3} - 119246 a^{2} + 821481 a + 543950\bigr] \)
|
| 16.2-a2
| \( \bigl[a\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 5 a^{3} - 16 a^{2} - a + 8\) , \( -28 a^{3} + 61 a^{2} + 10 a - 28\bigr] \)
|
| 16.2-a3
| \( \bigl[a\) , \( -1\) , \( a^{2} - 2\) , \( -6 a^{3} + 3 a^{2} + 29 a - 20\) , \( -14 a^{3} + 10 a^{2} + 60 a - 39\bigr] \)
|
| 16.2-a4
| \( \bigl[a\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( -2 a^{3} - a^{2} + 11 a - 5\) , \( -4 a^{3} + a^{2} + 19 a - 15\bigr] \)
|
| 16.2-a5
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -8 a^{3} - 22 a^{2} - 8 a + 8\) , \( 4 a^{3} + 8 a^{2} - 4 a - 8\bigr] \)
|
| 16.2-a6
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -88 a^{3} - 182 a^{2} + 42 a + 88\) , \( -1472 a^{3} - 3126 a^{2} + 652 a + 1372\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 8 & 4 & 8 \\
4 & 1 & 2 & 8 & 4 & 8 \\
2 & 2 & 1 & 4 & 2 & 4 \\
8 & 8 & 4 & 1 & 2 & 4 \\
4 & 4 & 2 & 2 & 1 & 2 \\
8 & 8 & 4 & 4 & 2 & 1
\end{array}\right)\)
