Elliptic curves in class 169.5-b over 6.6.434581.1
Isogeny class 169.5-b contains
4 curves linked by isogenies of
degrees dividing 39.
| Curve label |
Weierstrass Coefficients |
| 169.5-b1
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 14 a^{2} + a + 5\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( -988 a^{5} + 363 a^{4} + 6458 a^{3} + 2268 a^{2} - 8360 a - 5598\) , \( -93198 a^{5} + 141197 a^{4} + 423237 a^{3} - 233591 a^{2} - 410935 a - 59295\bigr] \)
|
| 169.5-b2
| \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 2\) , \( -a^{5} + a^{4} + 5 a^{3} - 4 a\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a - 1\) , \( -4615 a^{5} + 6477 a^{4} + 22822 a^{3} - 9642 a^{2} - 26598 a - 8423\) , \( -357233 a^{5} + 457061 a^{4} + 1749388 a^{3} - 528206 a^{2} - 1762650 a - 502392\bigr] \)
|
| 169.5-b3
| \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( -2 a^{5} + 6 a^{4} + 3 a^{3} - 14 a^{2} + a + 5\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 4 a - 2\) , \( 2 a^{5} + 3 a^{4} - 17 a^{3} - 17 a^{2} + 10 a + 7\) , \( 17 a^{5} - 11 a^{4} - 85 a^{3} - 26 a^{2} + 38 a + 14\bigr] \)
|
| 169.5-b4
| \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -a^{5} + 3 a^{4} + a^{3} - 7 a^{2} + 2 a + 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( -a^{5} - 2 a^{4} + 10 a^{3} + 12 a^{2} - 13 a - 7\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 6 a\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 13 & 39 \\
3 & 1 & 39 & 13 \\
13 & 39 & 1 & 3 \\
39 & 13 & 3 & 1
\end{array}\right)\)
