Elliptic curves in class 49.1-e over 6.6.485125.1
Isogeny class 49.1-e contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 49.1-e1
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( -a^{4} + 3 a^{2} + 2 a\) , \( a^{3} - 3 a - 1\) , \( a^{5} - 2 a^{4} - 8 a^{3} + 8 a^{2} + 15 a + 2\) , \( 7 a^{5} - 19 a^{4} - 15 a^{3} + 62 a^{2} - 24 a - 2\bigr] \)
|
| 49.1-e2
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 5 a - 1\) , \( -a^{4} + a^{3} + 3 a^{2} - 3 a - 2\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 4 a\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 4 a + 1\) , \( -5 a^{5} + 14 a^{4} + 8 a^{3} - 44 a^{2} + 28 a - 5\bigr] \)
|
| 49.1-e3
| \( \bigl[a^{4} - 4 a^{2} - a + 2\) , \( a^{4} - 4 a^{2} + 2\) , \( -2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 7 a + 3\) , \( 1286 a^{5} - 1768 a^{4} - 6218 a^{3} + 6370 a^{2} + 6394 a - 2350\) , \( -41543 a^{5} + 53994 a^{4} + 204324 a^{3} - 189619 a^{2} - 217635 a + 56419\bigr] \)
|
| 49.1-e4
| \( \bigl[a^{5} - 5 a^{3} + 4 a\) , \( -a^{5} + a^{4} + 6 a^{3} - 4 a^{2} - 7 a + 1\) , \( -a^{5} + a^{4} + 5 a^{3} - 3 a^{2} - 5 a + 1\) , \( -67 a^{5} + 147 a^{4} + 136 a^{3} - 479 a^{2} + 248 a - 44\) , \( -611 a^{5} + 1384 a^{4} + 1064 a^{3} - 4447 a^{2} + 2879 a - 492\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 5 & 15 \\
3 & 1 & 15 & 5 \\
5 & 15 & 1 & 3 \\
15 & 5 & 3 & 1
\end{array}\right)\)
