Elliptic curves in class 10.2-a over 4.4.19796.1
Isogeny class 10.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 10.2-a1
| \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 27 a^{3} - 81 a^{2} - 43 a + 139\) , \( -152 a^{3} + 424 a^{2} + 292 a - 653\bigr] \)
|
| 10.2-a2
| \( \bigl[a^{2} - a - 3\) , \( -a^{3} + a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 5 a + 1\) , \( 62 a^{3} - 171 a^{2} - 123 a + 259\) , \( 292 a^{3} - 776 a^{2} - 623 a + 1099\bigr] \)
|
| 10.2-a3
| \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( -5 a^{3} + 18 a^{2} + 25 a - 46\) , \( 10 a^{3} - 11 a^{2} - 32 a + 36\bigr] \)
|
| 10.2-a4
| \( \bigl[a^{3} - 2 a^{2} - 3 a + 5\) , \( a^{3} - 3 a^{2} - 4 a + 8\) , \( a^{3} - 2 a^{2} - 4 a + 4\) , \( -8 a^{3} - 31 a^{2} + 53\) , \( -90 a^{3} - 191 a^{2} + 103 a + 277\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 2 & 2 \\
2 & 1 & 4 & 4 \\
2 & 4 & 1 & 4 \\
2 & 4 & 4 & 1
\end{array}\right)\)
