Elliptic curves in class 71.1-c over 6.6.703493.1
Isogeny class 71.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.1-c1
| \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a^{2} + 3 a - 2\) , \( -a^{5} + 7 a^{3} + a^{2} - 9 a - 4\) , \( a^{2} + a - 1\) , \( -15 a^{5} - 9 a^{4} + 70 a^{3} + 20 a^{2} - 72 a - 28\) , \( -111 a^{5} - 50 a^{4} + 481 a^{3} - 2 a^{2} - 394 a - 1\bigr] \)
|
| 71.1-c2
| \( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( -a^{4} + 3 a^{2} + 1\) , \( -7 a^{5} + 5 a^{4} + 39 a^{3} - 20 a^{2} - 41 a + 4\bigr] \)
|
| 71.1-c3
| \( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( -165 a^{5} + 124 a^{4} + 1015 a^{3} - 622 a^{2} - 1135 a + 136\) , \( -2020 a^{5} + 1467 a^{4} + 12003 a^{3} - 6970 a^{2} - 13017 a + 1579\bigr] \)
|
| 71.1-c4
| \( \bigl[a + 1\) , \( 2 a^{5} - 2 a^{4} - 11 a^{3} + 9 a^{2} + 10 a - 2\) , \( a^{2} - 2\) , \( 10 a^{5} - 11 a^{4} - 45 a^{3} + 28 a^{2} + 45 a - 4\) , \( -16 a^{5} + 45 a^{4} - a^{3} - 49 a^{2} + 6 a - 1\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
