Elliptic curves in class 27.1-n over 6.6.1397493.1
Isogeny class 27.1-n contains
3 curves linked by isogenies of
degrees dividing 9.
Curve label |
Weierstrass Coefficients |
27.1-n1
| \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( 88 a^{5} - 247 a^{4} - 295 a^{3} + 791 a^{2} + 390 a - 424\) , \( -462 a^{5} + 1310 a^{4} + 1568 a^{3} - 4227 a^{2} - 2118 a + 2250\bigr] \)
|
27.1-n2
| \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -2 a^{5} + 8 a^{4} + 5 a^{3} - 24 a^{2} - 10 a + 11\) , \( a^{5} + a^{4} - 3 a^{3} - 8 a^{2} - 2 a + 4\bigr] \)
|
27.1-n3
| \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -12 a^{5} + 33 a^{4} + 35 a^{3} - 114 a^{2} - 55 a + 56\) , \( -41 a^{5} + 22 a^{4} + 140 a^{3} - 52 a^{2} - 98 a + 42\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrr}
1 & 3 & 9 \\
3 & 1 & 3 \\
9 & 3 & 1
\end{array}\right)\)