Isogeny class 17.2-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 17.2-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a + 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 71 a^{3} + 86 a^{2} - 241 a - 307\) , \( -545 a^{3} - 262 a^{2} + 1871 a + 864\bigr] \)
|
| 17.2-b2
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( a^{3} + a^{2} - 2 a - 1\) , \( a^{2} - 1\) , \( 2 a^{3} + 4 a^{2} - 2 a - 3\) , \( a^{3} + 2 a^{2} + a\bigr] \)
|
| 17.2-b3
| \( \bigl[a^{3} + a^{2} - 2 a - 2\) , \( 1\) , \( a^{3} - 2 a + 1\) , \( -3 a^{3} + 2 a^{2} + 11 a - 7\) , \( -a^{3} + a^{2} + 4 a - 3\bigr] \)
|
| 17.2-b4
| \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 2 a - 3\) , \( a^{2} + a - 1\) , \( 2 a^{3} - 52 a^{2} + 5 a + 29\) , \( 112 a^{3} - 458 a^{2} - 64 a + 266\bigr] \)
|
| 17.2-b5
| \( \bigl[a^{2} - 2\) , \( -a^{3} + 4 a\) , \( a^{2} + a - 1\) , \( 6 a^{3} - 5 a^{2} - 34 a - 22\) , \( 24 a^{3} - 9 a^{2} - 138 a - 90\bigr] \)
|
| 17.2-b6
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 1\) , \( 8 a^{3} + 7 a^{2} - 31 a - 23\) , \( 6 a^{3} + 5 a^{2} - 23 a - 18\bigr] \)
|
| 17.2-b7
| \( \bigl[a^{3} - 3 a\) , \( -a^{3} - a^{2} + 3 a + 3\) , \( a^{3} - 2 a + 1\) , \( -6 a^{3} - 7 a^{2} + 46 a - 27\) , \( -38 a^{3} + 19 a^{2} + 166 a - 136\bigr] \)
|
| 17.2-b8
| \( \bigl[a\) , \( -a^{3} + 3 a + 1\) , \( a + 1\) , \( -2 a^{3} - a^{2} + 10 a - 5\) , \( -4 a^{2} + 9 a - 5\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 12 & 6 & 4 & 2 & 12 & 4 & 3 \\
12 & 1 & 2 & 3 & 6 & 4 & 12 & 4 \\
6 & 2 & 1 & 6 & 3 & 2 & 6 & 2 \\
4 & 3 & 6 & 1 & 2 & 12 & 4 & 12 \\
2 & 6 & 3 & 2 & 1 & 6 & 2 & 6 \\
12 & 4 & 2 & 12 & 6 & 1 & 3 & 4 \\
4 & 12 & 6 & 4 & 2 & 3 & 1 & 12 \\
3 & 4 & 2 & 12 & 6 & 4 & 12 & 1
\end{array}\right)\)
