Elliptic curves in class 71.3-c over 6.6.300125.1
Isogeny class 71.3-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.3-c1
| \( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 9\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 10 a^{2} + 12 a + 6\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( 301 a^{5} - 10 a^{4} - 2223 a^{3} - 1411 a^{2} + 1326 a + 389\) , \( 2885 a^{5} - 180 a^{4} - 21196 a^{3} - 12957 a^{2} + 12811 a + 3947\bigr] \)
|
| 71.3-c2
| \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( -a^{2} + a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a - 1\) , \( 8 a^{5} - a^{4} - 59 a^{3} - 34 a^{2} + 38 a + 18\) , \( 20 a^{5} - 5 a^{4} - 144 a^{3} - 69 a^{2} + 91 a + 29\bigr] \)
|
| 71.3-c3
| \( \bigl[-6 a^{5} + 2 a^{4} + 43 a^{3} + 17 a^{2} - 28 a - 6\) , \( -a^{2} + a + 3\) , \( a^{5} - a^{4} - 6 a^{3} + a^{2} + 3 a - 1\) , \( 48 a^{5} - 11 a^{4} - 344 a^{3} - 169 a^{2} + 198 a + 53\) , \( 315 a^{5} - 72 a^{4} - 2261 a^{3} - 1115 a^{2} + 1350 a + 413\bigr] \)
|
| 71.3-c4
| \( \bigl[-6 a^{5} + a^{4} + 44 a^{3} + 23 a^{2} - 28 a - 9\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 10 a^{2} + 12 a + 6\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 2\) , \( -4 a^{5} + 55 a^{4} - 43 a^{3} - 296 a^{2} + 126 a + 59\) , \( -181 a^{5} + 461 a^{4} + 739 a^{3} - 1746 a^{2} + 376 a + 244\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 3 & 2 \\
6 & 1 & 2 & 3 \\
3 & 2 & 1 & 6 \\
2 & 3 & 6 & 1
\end{array}\right)\)
