Elliptic curves in class 4.2-c over 4.4.17428.1
Isogeny class 4.2-c contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 4.2-c1
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 4 a\) , \( 125 a^{3} + 180 a^{2} - 346 a - 357\) , \( 7601 a^{3} + 10450 a^{2} - 20942 a - 19415\bigr] \)
|
| 4.2-c2
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - a^{2} - 5 a + 1\) , \( a^{3} - 4 a\) , \( -115 a^{3} - 160 a^{2} + 314 a + 298\) , \( 1398 a^{3} + 1912 a^{2} - 3856 a - 3536\bigr] \)
|
| 4.2-c3
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( 12 a^{3} + 2 a^{2} - 64 a - 32\) , \( -746 a^{3} - 395 a^{2} + 3877 a + 2940\bigr] \)
|
| 4.2-c4
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} - a + 4\) , \( a^{3} - 3 a - 1\) , \( -118 a^{3} - 38 a^{2} + 606 a + 333\) , \( 20036 a^{3} + 10735 a^{2} - 104175 a - 79746\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
