Elliptic curves in class 11.2-a over 6.6.1922000.1
Isogeny class 11.2-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 11.2-a1
| \( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( 2 a^{5} - 5 a^{4} - 9 a^{3} + 12 a^{2} + 9 a + 1\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( a^{5} - 8 a^{4} + 8 a^{3} + 23 a^{2} - 24 a - 8\) , \( 5 a^{5} - 7 a^{4} - 19 a^{3} + 15 a^{2} + 16 a + 3\bigr] \)
|
| 11.2-a2
| \( \bigl[a^{2} - a - 1\) , \( -2 a^{5} + 3 a^{4} + 14 a^{3} - 3 a^{2} - 21 a - 8\) , \( 2 a^{5} - 2 a^{4} - 17 a^{3} + 2 a^{2} + 26 a + 6\) , \( 4 a^{5} - a^{4} - 33 a^{3} - 20 a^{2} + 28 a + 11\) , \( -82 a^{5} + 109 a^{4} + 636 a^{3} - 123 a^{2} - 1051 a - 369\bigr] \)
|
| 11.2-a3
| \( \bigl[0\) , \( a^{5} - a^{4} - 9 a^{3} + a^{2} + 17 a + 4\) , \( 1\) , \( 2 a^{5} - 7 a^{4} - 3 a^{3} + 15 a^{2} - 1\) , \( 5 a^{5} - 13 a^{4} - 18 a^{3} + 23 a^{2} + 20 a + 3\bigr] \)
|
| 11.2-a4
| \( \bigl[-a^{5} + 2 a^{4} + 6 a^{3} - 4 a^{2} - 9 a - 1\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 2\) , \( 18 a^{5} - 44 a^{4} - 86 a^{3} + 111 a^{2} + 88 a + 14\) , \( -64 a^{5} + 144 a^{4} + 321 a^{3} - 328 a^{2} - 291 a - 48\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
