Elliptic curves in class 18.1-a over \(\Q(\sqrt{7}) \)
Isogeny class 18.1-a contains
8 curves linked by isogenies of
degrees dividing 16.
Curve label |
Weierstrass Coefficients |
18.1-a1
| \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -6732 a + 17809\) , \( 429164 a - 1135465\bigr] \)
|
18.1-a2
| \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 16 a + 47\) , \( -1313 a - 3476\bigr] \)
|
18.1-a3
| \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 6731 a + 17812\) , \( 429164 a + 1135461\bigr] \)
|
18.1-a4
| \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2274 a - 6013\) , \( 59627 a + 157758\bigr] \)
|
18.1-a5
| \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -944 a - 2493\) , \( -25533 a - 67556\bigr] \)
|
18.1-a6
| \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -32559 a - 86158\) , \( 5180690 a + 13706871\bigr] \)
|
18.1-a7
| \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 2273 a - 6016\) , \( 59627 a - 157762\bigr] \)
|
18.1-a8
| \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 32558 a - 86161\) , \( 5180690 a - 13706875\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\
8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\
16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\
8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\
4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\
16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\
2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\
4 & 8 & 16 & 8 & 4 & 16 & 2 & 1
\end{array}\right)\)