Elliptic curves in class 31.1-b over 5.5.138136.1
Isogeny class 31.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 31.1-b1
| \( \bigl[2 a^{4} - a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 4\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 3 a + 9\) , \( -22 a^{4} - 7 a^{3} + 147 a^{2} + 104 a - 84\) , \( -111 a^{4} + 64 a^{3} + 639 a^{2} - 5 a - 164\bigr] \)
|
| 31.1-b2
| \( \bigl[2 a^{4} - a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 4\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 3 a + 9\) , \( 478 a^{4} - 327 a^{3} - 2698 a^{2} + 279 a + 586\) , \( 6855 a^{4} - 4448 a^{3} - 38942 a^{2} + 2699 a + 9031\bigr] \)
|
| 31.1-b3
| \( \bigl[a^{4} - 6 a^{2} - 3 a + 2\) , \( a^{2} - a - 4\) , \( a + 1\) , \( -24 a^{4} + 11 a^{3} + 150 a^{2} + 8 a - 92\) , \( 35 a^{4} - 17 a^{3} - 219 a^{2} - 8 a + 136\bigr] \)
|
| 31.1-b4
| \( \bigl[a^{4} - 7 a^{2} - a + 6\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 5 a + 9\) , \( 2 a^{4} - a^{3} - 12 a^{2} - a + 7\) , \( -60 a^{4} - 186 a^{3} + 53 a^{2} + 288 a - 137\) , \( 1157 a^{4} + 1274 a^{3} - 2298 a^{2} + 66 a + 302\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 2 & 6 \\
3 & 1 & 6 & 2 \\
2 & 6 & 1 & 3 \\
6 & 2 & 3 & 1
\end{array}\right)\)
