Elliptic curves in class 8.1-a over 4.4.13768.1
Isogeny class 8.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 8.1-a1
| \( \bigl[a^{2} - 3\) , \( -a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 86 a^{3} - 109 a^{2} - 667 a - 282\) , \( 881 a^{3} - 1467 a^{2} - 7702 a - 3314\bigr] \)
|
| 8.1-a2
| \( \bigl[a^{2} - 3\) , \( a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 7 a^{3} - 14 a^{2} - 17 a + 21\) , \( -8 a^{3} + 27 a^{2} - 16 a - 1\bigr] \)
|
| 8.1-a3
| \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - 5 a - 2\) , \( -24 a^{3} + 34 a^{2} + 110 a - 108\) , \( -144 a^{3} + 217 a^{2} + 608 a - 588\bigr] \)
|
| 8.1-a4
| \( \bigl[a^{3} - 5 a - 1\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - 3\) , \( -5 a^{3} + 6 a^{2} + 20 a - 8\) , \( -3 a^{2} + 3 a + 10\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
