Elliptic curves in class 4.2-a over 4.4.17428.1
Isogeny class 4.2-a contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 4.2-a1
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( -a^{3} + 4 a + 2\) , \( a^{2} - 3\) , \( -2 a^{2} + 8 a + 8\) , \( 31 a^{3} - 95 a^{2} + 22 a + 90\bigr] \)
|
| 4.2-a2
| \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 1\) , \( a^{3} + 2 a^{2} - 3 a - 2\) , \( 2 a^{3} + 5 a^{2} - 7 a - 8\bigr] \)
|
| 4.2-a3
| \( \bigl[1\) , \( a^{3} + a^{2} - 5 a - 5\) , \( a^{2} - 2\) , \( 112 a^{3} - 299 a^{2} - 16 a + 227\) , \( -1762 a^{3} + 5119 a^{2} - 402 a - 4355\bigr] \)
|
| 4.2-a4
| \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -20 a^{3} - 27 a^{2} + 54 a + 51\) , \( -111 a^{3} - 152 a^{2} + 306 a + 281\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
