Elliptic curves in class 5000.3-a over \(\Q(\sqrt{-1}) \)
Isogeny class 5000.3-a contains
10 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 5000.3-a1
| \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -751 i - 1082\) , \( 13990 i + 11750\bigr] \)
|
| 5000.3-a2
| \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 750 i - 1082\) , \( -15072 i + 11000\bigr] \)
|
| 5000.3-a3
| \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -82\) , \( -572 i\bigr] \)
|
| 5000.3-a4
| \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1500 i - 832\) , \( 3428 i + 25500\bigr] \)
|
| 5000.3-a5
| \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -1501 i - 832\) , \( -4260 i + 27000\bigr] \)
|
| 5000.3-a6
| \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 43\) , \( 115 i\bigr] \)
|
| 5000.3-a7
| \( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( 125\bigr] \)
|
| 5000.3-a8
| \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 668\) , \( 6990 i\bigr] \)
|
| 5000.3-a9
| \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 12000 i - 17332\) , \( -937572 i + 718500\bigr] \)
|
| 5000.3-a10
| \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -12001 i - 17332\) , \( 920240 i + 730500\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrrrr}
1 & 4 & 2 & 8 & 2 & 4 & 8 & 8 & 8 & 2 \\
4 & 1 & 2 & 2 & 8 & 4 & 8 & 8 & 2 & 8 \\
2 & 2 & 1 & 4 & 4 & 2 & 4 & 4 & 4 & 4 \\
8 & 2 & 4 & 1 & 16 & 8 & 16 & 16 & 4 & 16 \\
2 & 8 & 4 & 16 & 1 & 8 & 16 & 16 & 16 & 4 \\
4 & 4 & 2 & 8 & 8 & 1 & 2 & 2 & 8 & 8 \\
8 & 8 & 4 & 16 & 16 & 2 & 1 & 4 & 16 & 16 \\
8 & 8 & 4 & 16 & 16 & 2 & 4 & 1 & 16 & 16 \\
8 & 2 & 4 & 4 & 16 & 8 & 16 & 16 & 1 & 16 \\
2 & 8 & 4 & 16 & 4 & 8 & 16 & 16 & 16 & 1
\end{array}\right)\)
