Elliptic curves in class 676.5-g over \(\Q(\sqrt{17}) \)
Isogeny class 676.5-g contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 676.5-g1
| \( \bigl[1\) , \( a\) , \( a + 1\) , \( -255 a - 453\) , \( 131172 a + 205016\bigr] \)
|
| 676.5-g2
| \( \bigl[1\) , \( a\) , \( a + 1\) , \( 30 a + 47\) , \( -4839 a - 7556\bigr] \)
|
| 676.5-g3
| \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -196 a - 747\) , \( -3157 a + 1911\bigr] \)
|
| 676.5-g4
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -970 a - 1515\) , \( 13672 a + 21349\bigr] \)
|
| 676.5-g5
| \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -11 a - 37\) , \( -27 a - 99\bigr] \)
|
| 676.5-g6
| \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -26 a - 597\) , \( 537 a + 5409\bigr] \)
|
| 676.5-g7
| \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -261 a - 357\) , \( -2915 a - 4715\bigr] \)
|
| 676.5-g8
| \( \bigl[1\) , \( a\) , \( a + 1\) , \( 1635 a - 4253\) , \( -22418 a + 57566\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
