Elliptic curves in class 19.2-b over 5.5.138136.1
Isogeny class 19.2-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 19.2-b1
| \( \bigl[a^{4} - 6 a^{2} - 3 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - a\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 4 a + 9\) , \( -2 a^{4} + a^{3} + 12 a^{2} - 4\) , \( -5 a^{4} + 2 a^{3} + 30 a^{2} + 5 a - 14\bigr] \)
|
| 19.2-b2
| \( \bigl[2 a^{4} - 13 a^{2} - 5 a + 8\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 3 a + 7\) , \( 4 a^{4} - a^{3} - 25 a^{2} - 5 a + 13\) , \( 2 a^{4} - 6 a^{3} - 16 a^{2} + 9 a - 3\) , \( -12 a^{4} - 9 a^{3} + 28 a^{2} - 10 a - 4\bigr] \)
|
| 19.2-b3
| \( \bigl[a^{4} - 6 a^{2} - 3 a + 2\) , \( -a^{4} + a^{3} + 5 a^{2} - a\) , \( 3 a^{4} - a^{3} - 18 a^{2} - 4 a + 9\) , \( -92 a^{4} + 46 a^{3} + 572 a^{2} + 15 a - 354\) , \( -480 a^{4} + 249 a^{3} + 3002 a^{2} + 9 a - 1939\bigr] \)
|
| 19.2-b4
| \( \bigl[a^{4} - 7 a^{2} - a + 6\) , \( -a^{3} + a^{2} + 4 a\) , \( a^{4} - 6 a^{2} - 3 a + 3\) , \( -78 a^{4} + 76 a^{3} + 359 a^{2} + 77 a - 286\) , \( -955 a^{4} + 1558 a^{3} + 3330 a^{2} - 1418 a - 1343\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
