Elliptic curves in class 3.1-a over 6.6.1387029.1
Isogeny class 3.1-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 3.1-a1
| \( \bigl[a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( -a^{3} + 3 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} + 2\) , \( -36 a^{5} + 78 a^{4} + 148 a^{3} - 240 a^{2} - 139 a + 52\) , \( 1321 a^{5} - 3017 a^{4} - 4761 a^{3} + 8339 a^{2} + 4721 a - 1803\bigr] \)
|
| 3.1-a2
| \( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 3 a + 4\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 2 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( -12 a^{5} + 38 a^{4} + 27 a^{3} - 119 a^{2} - 8 a + 52\) , \( 316 a^{5} - 857 a^{4} - 871 a^{3} + 2585 a^{2} + 396 a - 1144\bigr] \)
|
| 3.1-a3
| \( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 3 a + 4\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} - 2 a\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( 23 a^{5} - 67 a^{4} - 58 a^{3} + 211 a^{2} + 27 a - 93\) , \( 82 a^{5} - 231 a^{4} - 216 a^{3} + 712 a^{2} + 98 a - 317\bigr] \)
|
| 3.1-a4
| \( \bigl[a^{4} - a^{3} - 3 a^{2} + a + 1\) , \( -a^{3} + 3 a\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} + 2\) , \( -96 a^{5} + 218 a^{4} + 353 a^{3} - 610 a^{2} - 349 a + 132\) , \( 551 a^{5} - 1250 a^{4} - 2010 a^{3} + 3487 a^{2} + 1985 a - 757\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
