Elliptic curves in class 16.1-a over 4.4.4752.1
Isogeny class 16.1-a contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 16.1-a1
| \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 18 a^{3} - 23 a^{2} - 52 a - 13\) , \( -41 a^{3} + 22 a^{2} + 184 a + 38\bigr] \)
|
| 16.1-a2
| \( \bigl[0\) , \( a^{3} - 2 a^{2} - a + 2\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( -49 a^{3} + 108 a^{2} + 124 a - 223\bigr] \)
|
| 16.1-a3
| \( \bigl[0\) , \( -a^{3} + 2 a^{2} + a - 2\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( 49 a^{3} - 108 a^{2} - 124 a + 223\bigr] \)
|
| 16.1-a4
| \( \bigl[a^{3} - 4 a - 1\) , \( a\) , \( 0\) , \( 17 a^{3} - 19 a^{2} - 45 a - 14\) , \( 72 a^{3} - 39 a^{2} - 316 a - 71\bigr] \)
|
| 16.1-a5
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{2} - a - 1\) , \( -2 a^{3} + 4 a - 2\) , \( -6 a^{3} + 12 a - 4\bigr] \)
|
| 16.1-a6
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( a^{2} - a - 1\) , \( -27 a^{3} - 10 a^{2} + 49 a + 3\) , \( -218 a^{3} - 109 a^{2} + 385 a + 88\bigr] \)
|
| 16.1-a7
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - 4 a - 1\) , \( -3 a^{3} + a^{2} + 5 a - 3\) , \( 4 a^{3} - 9 a\bigr] \)
|
| 16.1-a8
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a\) , \( a^{3} - 4 a - 1\) , \( -28 a^{3} - 9 a^{2} + 50 a + 2\) , \( 191 a^{3} + 99 a^{2} - 337 a - 87\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 4 & 12 & 6 & 3 & 2 & 4 \\
12 & 1 & 3 & 4 & 2 & 4 & 6 & 12 \\
4 & 3 & 1 & 12 & 6 & 12 & 2 & 4 \\
12 & 4 & 12 & 1 & 2 & 4 & 6 & 3 \\
6 & 2 & 6 & 2 & 1 & 2 & 3 & 6 \\
3 & 4 & 12 & 4 & 2 & 1 & 6 & 12 \\
2 & 6 & 2 & 6 & 3 & 6 & 1 & 2 \\
4 & 12 & 4 & 3 & 6 & 12 & 2 & 1
\end{array}\right)\)
