Elliptic curves in class 14.1-c over \(\Q(\sqrt{42}) \)
Isogeny class 14.1-c contains
6 curves linked by isogenies of
degrees dividing 18.
Curve label |
Weierstrass Coefficients |
14.1-c1
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8871 a - 57416\) , \( 1135220 a + 7357190\bigr] \)
|
14.1-c2
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -31 a - 126\) , \( -480 a - 2986\bigr] \)
|
14.1-c3
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 229 a + 1559\) , \( 8920 a + 57933\bigr] \)
|
14.1-c4
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -1851 a - 11921\) , \( 84920 a + 550469\bigr] \)
|
14.1-c5
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -551 a - 3496\) , \( -19280 a - 124824\bigr] \)
|
14.1-c6
| \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -141991 a - 920136\) , \( 73736820 a + 477869318\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 9 & 3 & 6 & 18 & 2 \\
9 & 1 & 3 & 6 & 2 & 18 \\
3 & 3 & 1 & 2 & 6 & 6 \\
6 & 6 & 2 & 1 & 3 & 3 \\
18 & 2 & 6 & 3 & 1 & 9 \\
2 & 18 & 6 & 3 & 9 & 1
\end{array}\right)\)