Elliptic curves in class 2.1-a over 3.3.1957.1
Isogeny class 2.1-a contains
8 curves linked by isogenies of
degrees dividing 20.
| Curve label |
Weierstrass Coefficients |
| 2.1-a1
| \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( -6506 a^{2} + 26575 a - 22213\) , \( -1035967 a^{2} + 4186759 a - 3408020\bigr] \)
|
| 2.1-a2
| \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( -371 a^{2} + 1665 a - 1693\) , \( -17120 a^{2} + 67995 a - 52840\bigr] \)
|
| 2.1-a3
| \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( 44 a^{2} + 50 a - 503\) , \( 271 a^{2} + 400 a - 3450\bigr] \)
|
| 2.1-a4
| \( \bigl[a^{2} + a - 6\) , \( a^{2} - a - 6\) , \( 0\) , \( 4 a^{2} + 5 a - 33\) , \( 3 a^{2} + 9 a - 40\bigr] \)
|
| 2.1-a5
| \( \bigl[1\) , \( -a^{2} + a + 5\) , \( 1\) , \( -26 a^{2} + 100 a - 77\) , \( -198 a^{2} + 767 a - 549\bigr] \)
|
| 2.1-a6
| \( \bigl[1\) , \( -a^{2} + a + 5\) , \( 1\) , \( -a^{2} + 8\) , \( 2 a^{2} - 9 a + 9\bigr] \)
|
| 2.1-a7
| \( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( a^{2} + a - 5\) , \( 1076 a^{2} + 142 a - 9533\) , \( -38349 a^{2} - 4961 a + 339519\bigr] \)
|
| 2.1-a8
| \( \bigl[a + 1\) , \( a^{2} + a - 7\) , \( a^{2} + a - 5\) , \( 6 a^{2} + 2 a - 48\) , \( 7 a^{2} + 2 a - 59\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 5 & 10 & 4 & 20 & 4 & 20 \\
2 & 1 & 10 & 5 & 2 & 10 & 2 & 10 \\
5 & 10 & 1 & 2 & 20 & 4 & 20 & 4 \\
10 & 5 & 2 & 1 & 10 & 2 & 10 & 2 \\
4 & 2 & 20 & 10 & 1 & 5 & 4 & 20 \\
20 & 10 & 4 & 2 & 5 & 1 & 20 & 4 \\
4 & 2 & 20 & 10 & 4 & 20 & 1 & 5 \\
20 & 10 & 4 & 2 & 20 & 4 & 5 & 1
\end{array}\right)\)
