Elliptic curves in class 19.2-b over 6.6.1397493.1
Isogeny class 19.2-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 19.2-b1
| \( \bigl[a^{4} - 3 a^{3} - a^{2} + 6 a - 1\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( 0\) , \( -20 a^{5} + 76 a^{4} - 8 a^{3} - 164 a^{2} + 68 a - 8\) , \( 3 a^{5} - 44 a^{4} + 119 a^{3} + 36 a^{2} - 277 a + 52\bigr] \)
|
| 19.2-b2
| \( \bigl[a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 11 a - 4\) , \( -a^{4} + 4 a^{3} - 2 a^{2} - 7 a + 5\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 1\) , \( 2 a^{5} - 104 a^{4} + 135 a^{3} + 202 a^{2} - 111 a - 20\) , \( 368 a^{5} - 56 a^{4} - 1473 a^{3} - 288 a^{2} + 785 a - 89\bigr] \)
|
| 19.2-b3
| \( \bigl[a\) , \( a^{5} - 3 a^{4} - 4 a^{3} + 11 a^{2} + 7 a - 4\) , \( a^{5} - 2 a^{4} - 6 a^{3} + 8 a^{2} + 10 a - 4\) , \( -105 a^{5} + 429 a^{4} - 160 a^{3} - 856 a^{2} + 635 a - 90\) , \( 1119 a^{5} - 4610 a^{4} + 1797 a^{3} + 9200 a^{2} - 6931 a + 1005\bigr] \)
|
| 19.2-b4
| \( \bigl[a^{4} - 3 a^{3} - a^{2} + 6 a - 1\) , \( a^{4} - 4 a^{3} + 9 a - 1\) , \( 0\) , \( 5 a^{5} - 19 a^{4} + 2 a^{3} + 41 a^{2} - 17 a + 2\) , \( 0\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 1\)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
