Isogeny class 17.1-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 17.1-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{2} + 3\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -5 a^{3} - 9 a^{2} + 5 a + 9\) , \( -4 a^{3} - 7 a^{2} + 4 a + 6\bigr] \)
|
| 17.1-b2
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 1\) , \( 2 a^{2} + 3 a + 1\) , \( a^{3} + 2 a^{2} + a\bigr] \)
|
| 17.1-b3
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{3} - 2 a + 1\) , \( 8 a^{3} + 5 a^{2} - 29 a - 21\) , \( -9 a^{3} - 7 a^{2} + 30 a + 22\bigr] \)
|
| 17.1-b4
| \( \bigl[a^{2} - 2\) , \( a^{3} - 2 a\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -15 a^{3} + 4 a^{2} + 38 a - 40\) , \( -65 a^{3} + 8 a^{2} + 170 a - 124\bigr] \)
|
| 17.1-b5
| \( \bigl[a^{2} - 2\) , \( -a^{3} - a^{2} + 3 a + 2\) , \( a^{3} - 3 a + 1\) , \( 18 a^{3} - 33 a^{2} - 10 a + 18\) , \( 90 a^{3} - 160 a^{2} - 59 a + 84\bigr] \)
|
| 17.1-b6
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + 3 a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( -27 a^{3} - 88 a^{2} + 8 a + 41\) , \( 237 a^{3} + 260 a^{2} - 168 a - 180\bigr] \)
|
| 17.1-b7
| \( \bigl[a^{3} - 3 a\) , \( a + 1\) , \( a^{3} - 3 a + 1\) , \( 4 a^{3} + a^{2} - 10 a - 9\) , \( 9 a^{3} + 4 a^{2} - 27 a - 21\bigr] \)
|
| 17.1-b8
| \( \bigl[a\) , \( a^{2} + a - 1\) , \( a^{3} - 2 a + 1\) , \( 28 a^{3} + 6 a^{2} - 79 a - 53\) , \( 52 a^{3} - 20 a^{2} - 119 a - 58\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 4 & 2 & 6 & 12 & 12 & 4 & 3 \\
4 & 1 & 2 & 6 & 3 & 12 & 4 & 12 \\
2 & 2 & 1 & 3 & 6 & 6 & 2 & 6 \\
6 & 6 & 3 & 1 & 2 & 2 & 6 & 2 \\
12 & 3 & 6 & 2 & 1 & 4 & 12 & 4 \\
12 & 12 & 6 & 2 & 4 & 1 & 3 & 4 \\
4 & 4 & 2 & 6 & 12 & 3 & 1 & 12 \\
3 & 12 & 6 & 2 & 4 & 4 & 12 & 1
\end{array}\right)\)
