Elliptic curves in class 16.2-a over 4.4.11324.1
Isogeny class 16.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 16.2-a1
| \( \bigl[a^{2} + a - 2\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 6 a^{3} + 2 a^{2} - 22 a - 8\) , \( 19 a^{3} + 7 a^{2} - 84 a - 30\bigr] \)
|
| 16.2-a2
| \( \bigl[a^{2} + a - 2\) , \( -a\) , \( a^{2} + a - 2\) , \( -4 a^{3} - 4 a^{2} + 9 a + 1\) , \( 2 a^{3} + 3 a^{2} - 4 a - 3\bigr] \)
|
| 16.2-a3
| \( \bigl[a^{2} + a - 2\) , \( -a\) , \( a^{2} + a - 2\) , \( -49 a^{3} - 64 a^{2} + 99 a + 41\) , \( 408 a^{3} + 509 a^{2} - 892 a - 363\bigr] \)
|
| 16.2-a4
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 13 a^{3} - 15 a^{2} - 108 a - 35\) , \( -288 a^{3} - 212 a^{2} + 988 a + 366\bigr] \)
|
| 16.2-a5
| \( \bigl[a^{3} - 3 a\) , \( a^{2} - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 3 a^{3} - 18 a - 5\) , \( -a^{3} - 4 a^{2} - 6 a - 2\bigr] \)
|
| 16.2-a6
| \( \bigl[a^{3} - 3 a\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a\) , \( -32 a^{3} + 45 a^{2} + 149 a - 179\) , \( 254 a^{3} - 341 a^{2} - 1142 a + 1417\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 8 & 4 & 8 \\
2 & 1 & 2 & 4 & 2 & 4 \\
4 & 2 & 1 & 8 & 4 & 8 \\
8 & 4 & 8 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)
