Elliptic curves in class 25.2-a over 4.4.4205.1
Isogeny class 25.2-a contains
4 curves linked by isogenies of
degrees dividing 10.
Curve label |
Weierstrass Coefficients |
25.2-a1
| \( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -9 a^{3} - 33 a^{2} - 21 a + 7\) , \( -91 a^{3} - 175 a^{2} - 36 a + 28\bigr] \)
|
25.2-a2
| \( \bigl[a^{3} - a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 4 a + 2\) , \( -a^{3} + 2 a^{2} + 4 a\) , \( -214 a^{3} - 388 a^{2} - 41 a + 67\) , \( -7172 a^{3} - 13212 a^{2} - 1656 a + 2523\bigr] \)
|
25.2-a3
| \( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -12 a^{3} + 8 a^{2} + 77 a - 17\) , \( 95 a^{3} - 189 a^{2} - 282 a + 147\bigr] \)
|
25.2-a4
| \( \bigl[a\) , \( -a^{3} + a^{2} + 5 a\) , \( -a^{3} + 2 a^{2} + 4 a - 1\) , \( -2 a^{3} + 3 a^{2} + 7 a - 7\) , \( -a^{3} + a^{2} + 5 a - 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 10 & 5 \\
2 & 1 & 5 & 10 \\
10 & 5 & 1 & 2 \\
5 & 10 & 2 & 1
\end{array}\right)\)