Elliptic curves in class 605.3-b over \(\Q(\sqrt{5}) \)
Isogeny class 605.3-b contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 605.3-b1
| \( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( 49 \phi - 224\) , \( -1605 \phi + 529\bigr] \)
|
| 605.3-b2
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 935 \phi - 1322\) , \( -8620 \phi + 16554\bigr] \)
|
| 605.3-b3
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -2\) , \( -7 \phi + 10\bigr] \)
|
| 605.3-b4
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 260 \phi - 547\) , \( 3445 \phi - 5141\bigr] \)
|
| 605.3-b5
| \( \bigl[\phi\) , \( \phi + 1\) , \( 0\) , \( -831 \phi - 2149\) , \( -21782 \phi - 39180\bigr] \)
|
| 605.3-b6
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 35 \phi - 87\) , \( -210 \phi + 261\bigr] \)
|
| 605.3-b7
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -65 \phi - 17\) , \( 390 \phi - 159\bigr] \)
|
| 605.3-b8
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -140 \phi - 267\) , \( -1855 \phi - 1431\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\
3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\
4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\
6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\
12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\
2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\
12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\
4 & 12 & 4 & 6 & 3 & 2 & 12 & 1
\end{array}\right)\)
