Isogeny class 81.1-a contains
8 curves linked by isogenies of
degrees dividing 30.
| Curve label |
Weierstrass Coefficients |
| 81.1-a1
| \( \bigl[a^{2} + a - 1\) , \( 0\) , \( a\) , \( -5 a^{3} - 23 a^{2} - 28 a - 6\) , \( 264 a^{3} + 140 a^{2} - 825 a - 176\bigr] \)
|
| 81.1-a2
| \( \bigl[a^{2} + a - 1\) , \( 0\) , \( a\) , \( 10 a^{3} + 7 a^{2} - 28 a - 6\) , \( 30 a^{3} + 23 a^{2} - 78 a - 17\bigr] \)
|
| 81.1-a3
| \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( -14 a^{3} + 42 a - 26\) , \( -32 a^{3} + 96 a - 51\bigr] \)
|
| 81.1-a4
| \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a + 1\) , \( 1\) , \( a^{3} - 3 a + 4\) , \( -2 a^{3} + 6 a - 3\bigr] \)
|
| 81.1-a5
| \( \bigl[1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -17 a^{3} + 51 a - 32\) , \( 52 a^{3} - 156 a + 82\bigr] \)
|
| 81.1-a6
| \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -161 a^{3} - 131 a^{2} + 401 a + 86\) , \( -1640 a^{3} - 1355 a^{2} + 4084 a + 893\bigr] \)
|
| 81.1-a7
| \( \bigl[1\) , \( -1\) , \( a^{3} - 3 a + 1\) , \( -2 a^{3} + 6 a - 2\) , \( a^{3} - 3 a + 1\bigr] \)
|
| 81.1-a8
| \( \bigl[a + 1\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -2561 a^{3} - 2096 a^{2} + 6386 a + 1346\) , \( -98327 a^{3} - 81248 a^{2} + 244768 a + 53612\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 15 & 30 & 3 & 10 & 6 & 5 \\
2 & 1 & 30 & 15 & 6 & 5 & 3 & 10 \\
15 & 30 & 1 & 2 & 5 & 6 & 10 & 3 \\
30 & 15 & 2 & 1 & 10 & 3 & 5 & 6 \\
3 & 6 & 5 & 10 & 1 & 30 & 2 & 15 \\
10 & 5 & 6 & 3 & 30 & 1 & 15 & 2 \\
6 & 3 & 10 & 5 & 2 & 15 & 1 & 30 \\
5 & 10 & 3 & 6 & 15 & 2 & 30 & 1
\end{array}\right)\)
