Elliptic curves in class 18.1-a over \(\Q(\sqrt{34}) \)
Isogeny class 18.1-a contains
8 curves linked by isogenies of
degrees dividing 20.
| Curve label |
Weierstrass Coefficients |
| 18.1-a1
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -3410637 a - 19887245\) , \( -8775001088 a - 51166609211\bigr] \)
|
| 18.1-a2
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 8103718 a + 47252405\) , \( 556798743074 a + 3246666685985\bigr] \)
|
| 18.1-a3
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -61719832 a - 359885355\) , \( -413435180474 a - 2410720648967\bigr] \)
|
| 18.1-a4
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -220297 a - 1284525\) , \( -127690376 a - 744556427\bigr] \)
|
| 18.1-a5
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -25184377 a - 146848875\) , \( 161354769508 a + 940851899017\bigr] \)
|
| 18.1-a6
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -3467657 a - 20219725\) , \( -8482309192 a - 49459936843\bigr] \)
|
| 18.1-a7
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -24981417 a - 145665425\) , \( 164156817952 a + 957190508701\bigr] \)
|
| 18.1-a8
| \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -55482437 a - 323515405\) , \( -543123237520 a - 3166925470939\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 5 & 20 & 4 & 10 & 2 & 20 & 4 \\
5 & 1 & 4 & 20 & 2 & 10 & 4 & 20 \\
20 & 4 & 1 & 20 & 2 & 10 & 4 & 5 \\
4 & 20 & 20 & 1 & 10 & 2 & 5 & 4 \\
10 & 2 & 2 & 10 & 1 & 5 & 2 & 10 \\
2 & 10 & 10 & 2 & 5 & 1 & 10 & 2 \\
20 & 4 & 4 & 5 & 2 & 10 & 1 & 20 \\
4 & 20 & 5 & 4 & 10 & 2 & 20 & 1
\end{array}\right)\)
