Isogeny class 17.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 17.2-a1
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( 1\) , \( a^{3} - 2 a + 1\) , \( 5 a^{3} + 4 a^{2} - 17 a - 14\) , \( 9 a^{3} + 7 a^{2} - 31 a - 25\bigr] \)
|
| 17.2-a2
| \( \bigl[a^{2} - 2\) , \( a^{2} - a - 2\) , \( a^{2} + a - 1\) , \( 17 a^{3} + 15 a^{2} - 60 a - 51\) , \( 54 a^{3} + 42 a^{2} - 186 a - 145\bigr] \)
|
| 17.2-a3
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 4 a - 3\) , \( a^{2} + a - 1\) , \( 26 a^{3} + 20 a^{2} - 88 a - 68\) , \( 108 a^{3} + 83 a^{2} - 369 a - 283\bigr] \)
|
| 17.2-a4
| \( \bigl[a^{2} + a - 2\) , \( -a^{2} - a + 2\) , \( a^{2} + a - 1\) , \( 44 a^{3} + 32 a^{2} - 152 a - 113\) , \( 463 a^{3} + 364 a^{2} - 1582 a - 1245\bigr] \)
|
| 17.2-a5
| \( \bigl[a^{3} - 3 a\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 3 a + 1\) , \( -11 a^{3} - 14 a^{2} + 19 a + 14\) , \( -22 a^{3} - 36 a^{2} + 23 a + 27\bigr] \)
|
| 17.2-a6
| \( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( 3 a^{3} + 2 a^{2} - 12 a - 8\) , \( -3 a^{3} - 3 a^{2} + 9 a + 7\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 2 & 2 \\
2 & 1 & 2 & 2 & 4 & 4 \\
4 & 2 & 1 & 4 & 8 & 8 \\
4 & 2 & 4 & 1 & 8 & 8 \\
2 & 4 & 8 & 8 & 1 & 4 \\
2 & 4 & 8 & 8 & 4 & 1
\end{array}\right)\)
