Elliptic curves in class 17.1-a over 4.4.4913.1
Isogeny class 17.1-a contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 17.1-a1
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{3}{2}\) , \( a^{2} - 2 a - 2\) , \( \frac{1}{2} a^{3} - 2 a - \frac{1}{2}\) , \( -\frac{5}{2} a^{3} + 4 a^{2} + 5 a - \frac{1}{2}\) , \( -2 a^{3} + 6 a^{2} - 3 a - 1\bigr] \)
|
| 17.1-a2
| \( \bigl[-\frac{1}{2} a^{3} + a^{2} + 3 a - \frac{1}{2}\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( 26 a^{3} - 13 a^{2} - 161 a - 51\) , \( -134 a^{3} + 69 a^{2} + 839 a + 276\bigr] \)
|
| 17.1-a3
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -330 a^{3} + 330 a^{2} + 1650 a - 936\) , \( -4996 a^{3} + 4996 a^{2} + 24980 a - 13110\bigr] \)
|
| 17.1-a4
| \( \bigl[1\) , \( -1\) , \( 1\) , \( 330 a^{3} - 330 a^{2} - 1650 a - 606\) , \( 4996 a^{3} - 4996 a^{2} - 24980 a - 8114\bigr] \)
|
| 17.1-a5
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)
|
| 17.1-a6
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
|
| 17.1-a7
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
|
| 17.1-a8
| \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 16 & 16 & 8 & 4 & 8 & 2 \\
4 & 1 & 16 & 16 & 8 & 4 & 8 & 2 \\
16 & 16 & 1 & 4 & 2 & 4 & 8 & 8 \\
16 & 16 & 4 & 1 & 2 & 4 & 8 & 8 \\
8 & 8 & 2 & 2 & 1 & 2 & 4 & 4 \\
4 & 4 & 4 & 4 & 2 & 1 & 2 & 2 \\
8 & 8 & 8 & 8 & 4 & 2 & 1 & 4 \\
2 & 2 & 8 & 8 & 4 & 2 & 4 & 1
\end{array}\right)\)
