Elliptic curves in class 16.1-a over 4.4.7600.1
Isogeny class 16.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 16.1-a1
| \( \bigl[a^{2} + a - 5\) , \( -a^{2} + 6\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 11 a^{3} + 14 a^{2} - 61 a - 86\) , \( -31 a^{3} - 44 a^{2} + 172 a + 250\bigr] \)
|
| 16.1-a2
| \( \bigl[a^{2} + a - 5\) , \( -a^{3} - a^{2} + 5 a + 6\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -11 a^{3} + 14 a^{2} + 59 a - 86\) , \( 31 a^{3} - 44 a^{2} - 173 a + 250\bigr] \)
|
| 16.1-a3
| \( \bigl[0\) , \( a^{3} - 6 a\) , \( 0\) , \( -6 a^{3} - 17 a^{2} + 22 a + 68\) , \( 15 a^{3} + 33 a^{2} - 55 a - 116\bigr] \)
|
| 16.1-a4
| \( \bigl[0\) , \( -a^{3} + 6 a\) , \( 0\) , \( 6 a^{3} - 17 a^{2} - 22 a + 68\) , \( -15 a^{3} + 33 a^{2} + 55 a - 116\bigr] \)
|
| 16.1-a5
| \( \bigl[a^{3} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -4 a^{3} + 16 a^{2} + 17 a - 70\) , \( -3 a^{3} + 16 a^{2} + 20 a - 90\bigr] \)
|
| 16.1-a6
| \( \bigl[a^{3} - 4 a + 1\) , \( 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 3 a - 5\) , \( 2 a^{3} - 7 a - 3\bigr] \)
|
| 16.1-a7
| \( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( 2 a^{3} + 16 a^{2} - 9 a - 70\) , \( 3 a^{3} + 16 a^{2} - 21 a - 90\bigr] \)
|
| 16.1-a8
| \( \bigl[a^{3} - 4 a + 1\) , \( -a^{3} + 4 a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -3 a^{3} + a^{2} + 11 a - 5\) , \( -2 a^{3} + 6 a - 3\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 4 & 2 & 12 & 6 \\
3 & 1 & 12 & 4 & 12 & 6 & 4 & 2 \\
4 & 12 & 1 & 3 & 4 & 2 & 12 & 6 \\
12 & 4 & 3 & 1 & 12 & 6 & 4 & 2 \\
4 & 12 & 4 & 12 & 1 & 2 & 3 & 6 \\
2 & 6 & 2 & 6 & 2 & 1 & 6 & 3 \\
12 & 4 & 12 & 4 & 3 & 6 & 1 & 2 \\
6 & 2 & 6 & 2 & 6 & 3 & 2 & 1
\end{array}\right)\)
