Elliptic curves in class 21.1-a over 4.4.9909.1
Isogeny class 21.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 21.1-a1
| \( \bigl[a^{3} - 5 a - 2\) , \( a^{2} - 3\) , \( a\) , \( 72 a^{3} + 44 a^{2} - 417 a - 462\) , \( 786 a^{3} + 381 a^{2} - 4500 a - 4563\bigr] \)
|
| 21.1-a2
| \( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -13750 a^{3} + 16600 a^{2} + 62447 a - 34158\) , \( 1313070 a^{3} - 1585569 a^{2} - 5963840 a + 3262240\bigr] \)
|
| 21.1-a3
| \( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -13750 a^{3} + 16605 a^{2} + 62452 a - 34158\) , \( 1313123 a^{3} - 1585648 a^{2} - 5964098 a + 3262387\bigr] \)
|
| 21.1-a4
| \( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -930 a^{3} + 1070 a^{2} + 4157 a - 2268\) , \( 17576 a^{3} - 21717 a^{2} - 80504 a + 44128\bigr] \)
|
| 21.1-a5
| \( \bigl[1\) , \( a\) , \( a^{2} - 2\) , \( -50 a^{3} + 60 a^{2} + 227 a - 123\) , \( 382 a^{3} - 462 a^{2} - 1736 a + 949\bigr] \)
|
| 21.1-a6
| \( \bigl[a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( a^{2} - 3\) , \( -784 a^{3} - 509 a^{2} + 1519 a - 616\) , \( 18547 a^{3} + 24195 a^{2} - 19665 a + 1670\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 2 & 2 & 4 \\
2 & 1 & 2 & 4 & 4 & 2 \\
4 & 2 & 1 & 8 & 8 & 4 \\
2 & 4 & 8 & 1 & 4 & 8 \\
2 & 4 & 8 & 4 & 1 & 8 \\
4 & 2 & 4 & 8 & 8 & 1
\end{array}\right)\)
