Elliptic curves in class 45.1-e over 5.5.65657.1
Isogeny class 45.1-e contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 45.1-e1
| \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 5\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 11 a + 9\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( -14 a^{4} + 10 a^{3} - 3 a^{2} + 2 a - 7\) , \( -284 a^{4} + 587 a^{3} + 1227 a^{2} - 1161 a - 1194\bigr] \)
|
| 45.1-e2
| \( \bigl[-a^{4} + 2 a^{3} + 5 a^{2} - 7 a - 5\) , \( 3 a^{4} - 4 a^{3} - 13 a^{2} + 11 a + 9\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 5\) , \( -24 a^{4} + 30 a^{3} + 107 a^{2} - 73 a - 97\) , \( -172 a^{4} + 214 a^{3} + 809 a^{2} - 536 a - 735\bigr] \)
|
| 45.1-e3
| \( \bigl[a^{2} - a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 5\) , \( a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 2 a + 3\) , \( -2 a^{4} - a^{3} + 9 a^{2} + 10 a + 3\bigr] \)
|
| 45.1-e4
| \( \bigl[a^{2} - a - 1\) , \( 2 a^{4} - 2 a^{3} - 9 a^{2} + 6 a + 5\) , \( a^{3} - 4 a - 1\) , \( 40 a^{4} - 14 a^{3} - 166 a^{2} - 52 a - 17\) , \( 84 a^{4} + 35 a^{3} - 366 a^{2} - 370 a - 111\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
