Elliptic curves in class 605.2-b over \(\Q(\sqrt{5}) \)
Isogeny class 605.2-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 605.2-b1
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( 7 \phi + 3\bigr] \)
|
| 605.2-b2
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 65 \phi - 82\) , \( -390 \phi + 231\bigr] \)
|
| 605.2-b3
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 140 \phi - 407\) , \( 1855 \phi - 3286\bigr] \)
|
| 605.2-b4
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -935 \phi - 387\) , \( 8620 \phi + 7934\bigr] \)
|
| 605.2-b5
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -260 \phi - 287\) , \( -3445 \phi - 1696\bigr] \)
|
| 605.2-b6
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -35 \phi - 52\) , \( 210 \phi + 51\bigr] \)
|
| 605.2-b7
| \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( 832 \phi - 2982\) , \( 18800 \phi - 57148\bigr] \)
|
| 605.2-b8
| \( \bigl[\phi + 1\) , \( \phi - 1\) , \( \phi\) , \( -48 \phi - 177\) , \( 1428 \phi - 947\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
