Elliptic curves in class 18.1-f over \(\Q(\sqrt{34}) \)
Isogeny class 18.1-f contains
8 curves linked by isogenies of
degrees dividing 20.
| Curve label |
Weierstrass Coefficients |
| 18.1-f1
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -307 a - 6346\) , \( -15106 a - 223719\bigr] \)
|
| 18.1-f2
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 2088 a + 7104\) , \( 1636360 a + 9432569\bigr] \)
|
| 18.1-f3
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -12662 a - 73136\) , \( -1237372 a - 7090263\bigr] \)
|
| 18.1-f4
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -47 a - 266\) , \( -442 a - 2631\bigr] \)
|
| 18.1-f5
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4967 a - 31016\) , \( 459902 a + 2709765\bigr] \)
|
| 18.1-f6
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -687 a - 4266\) , \( -25658 a - 152455\bigr] \)
|
| 18.1-f7
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4927 a - 30766\) , \( 468086 a + 2758161\bigr] \)
|
| 18.1-f8
| \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -11307 a - 66186\) , \( -1602674 a - 9348007\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\
5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\
20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\
4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\
10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\
2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\
20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\
4 & 20 & 5 & 4 & 10 & 2 & 20 & 1
\end{array}\right)\)
