Elliptic curves in class 3.1-a over 5.5.89417.1
Isogeny class 3.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 3.1-a1
| \( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 978 a^{4} - 1249 a^{3} - 4424 a^{2} + 4612 a + 2327\) , \( -28873 a^{4} + 35329 a^{3} + 129230 a^{2} - 130011 a - 69785\bigr] \)
|
| 3.1-a2
| \( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 78 a^{4} - 94 a^{3} - 369 a^{2} + 372 a + 197\) , \( -134 a^{4} + 200 a^{3} + 466 a^{2} - 518 a - 272\bigr] \)
|
| 3.1-a3
| \( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( 3 a^{4} - 4 a^{3} - 14 a^{2} + 12 a + 12\) , \( 12 a^{4} - 14 a^{3} - 58 a^{2} + 55 a + 35\bigr] \)
|
| 3.1-a4
| \( \bigl[a^{4} - a^{3} - 5 a^{2} + 4 a + 6\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 4\) , \( a^{4} - 5 a^{2} + a + 5\) , \( -342 a^{4} + 421 a^{3} + 1526 a^{2} - 1548 a - 813\) , \( -1023 a^{4} + 1339 a^{3} + 4330 a^{2} - 4529 a - 2323\bigr] \)
|
| 3.1-a5
| \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 2\) , \( -5 a^{4} - 2 a^{3} + 38 a^{2} + 8 a - 71\) , \( -28 a^{4} - 8 a^{3} + 178 a^{2} + 38 a - 259\bigr] \)
|
| 3.1-a6
| \( \bigl[1\) , \( a^{4} - 5 a^{2} - a + 3\) , \( a^{2} - 1\) , \( -111 a^{4} + 209 a^{3} + 241 a^{2} - 350 a - 165\) , \( -1804 a^{4} + 3401 a^{3} + 3999 a^{2} - 5783 a - 2713\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 4 & 8 \\
2 & 1 & 4 & 2 & 2 & 4 \\
8 & 4 & 1 & 8 & 2 & 4 \\
4 & 2 & 8 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)
