Elliptic curves in class 27.1-e over 6.6.1397493.1
Isogeny class 27.1-e contains
3 curves linked by isogenies of
degrees dividing 9.
| Curve label |
Weierstrass Coefficients |
| 27.1-e1
| \( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} - a^{3} + 12 a^{2} - a - 4\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 3\) , \( -26 a^{5} + 83 a^{4} + 128 a^{3} - 275 a^{2} - 264 a + 63\) , \( 204 a^{5} - 422 a^{4} - 876 a^{3} + 1247 a^{2} + 1306 a - 299\bigr] \)
|
| 27.1-e2
| \( \bigl[a^{2} - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a\) , \( 1\) , \( 2 a^{5} - 6 a^{4} - 2 a^{3} + 13 a^{2} - 5 a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a\bigr] \)
|
| 27.1-e3
| \( \bigl[a^{2} - 2\) , \( -a^{4} + 3 a^{3} + 2 a^{2} - 8 a\) , \( 1\) , \( 17 a^{5} - 6 a^{4} - 77 a^{3} - 72 a^{2} - 20 a + 10\) , \( 217 a^{5} - 188 a^{4} - 1059 a^{3} - 159 a^{2} + 471 a - 76\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrr}
1 & 3 & 9 \\
3 & 1 & 3 \\
9 & 3 & 1
\end{array}\right)\)
