Elliptic curves in class 49.2-a over 4.4.725.1
Isogeny class 49.2-a contains
4 curves linked by isogenies of
degrees dividing 10.
| Curve label |
Weierstrass Coefficients |
| 49.2-a1
| \( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 427 a^{3} - 605 a^{2} - 535 a - 162\) , \( 6328 a^{3} - 10800 a^{2} - 5249 a + 192\bigr] \)
|
| 49.2-a2
| \( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -3 a^{3} + 5 a^{2} - 2\) , \( -18 a^{3} + 42 a^{2} - 2 a - 14\bigr] \)
|
| 49.2-a3
| \( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 2 a^{3} - 5 a^{2} + 3\) , \( -a^{3} + 2 a^{2} - 1\bigr] \)
|
| 49.2-a4
| \( \bigl[a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( 237 a^{3} - 560 a^{2} + 85 a + 103\) , \( 4228 a^{3} - 10047 a^{2} + 1135 a + 2839\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 5 & 10 & 2 \\
5 & 1 & 2 & 10 \\
10 & 2 & 1 & 5 \\
2 & 10 & 5 & 1
\end{array}\right)\)
