Elliptic curves in class 71.2-c over 6.6.300125.1
Isogeny class 71.2-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 71.2-c1
| \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 4\) , \( -4 a^{5} + 2 a^{4} + 28 a^{3} + 7 a^{2} - 18 a - 1\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 12 a + 5\) , \( -11 a^{5} + 17 a^{4} + 67 a^{3} - 64 a^{2} - 10 a + 12\) , \( 34 a^{5} - 62 a^{4} - 194 a^{3} + 257 a^{2} + a - 52\bigr] \)
|
| 71.2-c2
| \( \bigl[a^{5} - 7 a^{3} - 5 a^{2} + 3 a + 3\) , \( 3 a^{5} - a^{4} - 21 a^{3} - 8 a^{2} + 10 a + 1\) , \( a^{5} - 7 a^{3} - 5 a^{2} + 2 a + 2\) , \( 160 a^{5} - 32 a^{4} - 1154 a^{3} - 592 a^{2} + 710 a + 205\) , \( -79 a^{5} + 80 a^{4} + 491 a^{3} - 91 a^{2} - 150 a - 35\bigr] \)
|
| 71.2-c3
| \( \bigl[3 a^{5} - a^{4} - 21 a^{3} - 9 a^{2} + 13 a + 5\) , \( a^{2} - 2\) , \( -2 a^{5} + 15 a^{3} + 10 a^{2} - 9 a - 4\) , \( -5 a^{5} + 2 a^{4} + 37 a^{3} + 15 a^{2} - 25 a - 6\) , \( -2 a^{5} + a^{4} + 17 a^{3} + 9 a^{2} - 12 a - 4\bigr] \)
|
| 71.2-c4
| \( \bigl[-4 a^{5} + a^{4} + 29 a^{3} + 13 a^{2} - 18 a - 4\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 17 a - 5\) , \( -3 a^{5} + 23 a^{3} + 14 a^{2} - 16 a - 5\) , \( -1192 a^{5} + 784 a^{4} + 7943 a^{3} + 1280 a^{2} - 4145 a - 1190\) , \( -14256 a^{5} + 14083 a^{4} + 88506 a^{3} - 11460 a^{2} - 35243 a - 7572\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 6 & 2 & 3 \\
6 & 1 & 3 & 2 \\
2 & 3 & 1 & 6 \\
3 & 2 & 6 & 1
\end{array}\right)\)
