Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 8 & 4 & 2 & 4 \\
8 & 1 & 4 & 2 & 4 & 8 \\
8 & 4 & 1 & 2 & 4 & 8 \\
4 & 2 & 2 & 1 & 2 & 4 \\
2 & 4 & 4 & 2 & 1 & 2 \\
4 & 8 & 8 & 4 & 2 & 1
\end{array}\right)\)
Elliptic curves in class 16.2-a over 4.4.7232.1
Isogeny class 16.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 16.2-a1
| \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + 2 a^{2} - \frac{1}{2} a - 4\) , \( 0\) , \( \frac{19}{2} a^{3} - \frac{89}{2} a - 24\) , \( \frac{45}{2} a^{3} - 3 a^{2} - \frac{211}{2} a - 62\bigr] \)
|
| 16.2-a2
| \( \bigl[\frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( -\frac{1}{2} a^{3} + \frac{5}{2} a + 2\) , \( \frac{1}{2} a^{3} - \frac{3}{2} a - 1\) , \( a^{3} + 3 a^{2} + 3 a + 1\) , \( \frac{23}{2} a^{3} + 15 a^{2} - \frac{27}{2} a - 12\bigr] \)
|
| 16.2-a3
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a\) , \( a^{2} - 2\) , \( 15 a^{3} - 14 a^{2} - 101 a - 54\) , \( -73 a^{3} + 61 a^{2} + 440 a + 240\bigr] \)
|
| 16.2-a4
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( -\frac{1}{2} a^{3} + a^{2} + \frac{3}{2} a\) , \( a^{2} - 2\) , \( a^{2} - 6 a - 4\) , \( -a^{3} + a^{2} + 2 a\bigr] \)
|
| 16.2-a5
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( 107 a^{3} - 85 a^{2} - 636 a - 343\) , \( \frac{2723}{2} a^{3} - 1060 a^{2} - \frac{16203}{2} a - 4453\bigr] \)
|
| 16.2-a6
| \( \bigl[\frac{1}{2} a^{3} - a^{2} - \frac{1}{2} a + 1\) , \( \frac{1}{2} a^{3} - 2 a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 1\) , \( -58 a^{3} + 45 a^{2} + 344 a + 187\) , \( \frac{9623}{2} a^{3} - 3738 a^{2} - \frac{57277}{2} a - 15773\bigr] \)
|
