Elliptic curves in class 225.1-b over \(\Q(\sqrt{5}) \)
Isogeny class 225.1-b contains
10 curves linked by isogenies of
degrees dividing 32.
| Curve label |
Weierstrass Coefficients |
| 225.1-b1
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 16875 \phi - 55575\) , \( -2120029 \phi + 5229447\bigr] \)
|
| 225.1-b2
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -550 \phi - 550\) , \( 15946 \phi + 12097\bigr] \)
|
| 225.1-b3
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 0\) , \( -4 \phi - 3\bigr] \)
|
| 225.1-b4
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( 175 \phi + 175\) , \( 1081 \phi + 767\bigr] \)
|
| 225.1-b5
| \( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( 49 \phi - 100\) , \( -147 \phi + 243\bigr] \)
|
| 225.1-b6
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -25 \phi - 25\) , \( -119 \phi - 83\bigr] \)
|
| 225.1-b7
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -675 \phi - 675\) , \( 11171 \phi + 8547\bigr] \)
|
| 225.1-b8
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -400 \phi - 400\) , \( -6044 \phi - 4433\bigr] \)
|
| 225.1-b9
| \( \bigl[\phi + 1\) , \( \phi\) , \( \phi + 1\) , \( -10800 \phi - 10800\) , \( 758396 \phi + 571497\bigr] \)
|
| 225.1-b10
| \( \bigl[\phi\) , \( \phi - 1\) , \( \phi + 1\) , \( -16876 \phi - 38700\) , \( 2081328 \phi + 3131243\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrr}
1 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 4 \\
8 & 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 & 8 \\
32 & 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 & 32 \\
16 & 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 & 16 \\
8 & 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 & 8 \\
16 & 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 & 16 \\
4 & 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 & 4 \\
32 & 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 & 32 \\
2 & 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 & 2 \\
4 & 8 & 32 & 16 & 8 & 16 & 4 & 32 & 2 & 1
\end{array}\right)\)
