Elliptic curves in class 19.1-c over 4.4.8069.1
Isogeny class 19.1-c contains
4 curves linked by isogenies of
degrees dividing 6.
Curve label |
Weierstrass Coefficients |
19.1-c1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 5 a\) , \( 1\) , \( 85 a^{3} + 459 a^{2} - 366 a - 2135\) , \( -10862 a^{3} + 5071 a^{2} + 51661 a - 27097\bigr] \)
|
19.1-c2
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( -a^{3} + 5 a\) , \( 1\) , \( 40 a^{3} + 39 a^{2} - 181 a - 160\) , \( 261 a^{3} + 179 a^{2} - 1219 a - 762\bigr] \)
|
19.1-c3
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + 11 a^{2} + 19 a - 45\) , \( -13 a^{3} + 30 a^{2} + 74 a - 109\bigr] \)
|
19.1-c4
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( 4 a^{3} + 6 a^{2} - 11 a - 5\) , \( 7 a^{3} + 9 a^{2} - 18 a - 5\bigr] \)
|
Rank \(r\) satisfies \(0 \le r \le 1\)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)