Elliptic curves in class 18.1-b over \(\Q(\sqrt{7}) \)
Isogeny class 18.1-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 18.1-b1
| \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -6732 a + 17812\) , \( -429165 a + 1135461\bigr] \)
|
| 18.1-b2
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 16 a + 44\) , \( 1312 a + 3472\bigr] \)
|
| 18.1-b3
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 6731 a + 17809\) , \( -429165 a - 1135465\bigr] \)
|
| 18.1-b4
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -2274 a - 6016\) , \( -59628 a - 157762\bigr] \)
|
| 18.1-b5
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -944 a - 2496\) , \( 25532 a + 67552\bigr] \)
|
| 18.1-b6
| \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -32559 a - 86161\) , \( -5180691 a - 13706875\bigr] \)
|
| 18.1-b7
| \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 2273 a - 6013\) , \( -59628 a + 157758\bigr] \)
|
| 18.1-b8
| \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( 32558 a - 86158\) , \( -5180691 a + 13706871\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\
8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\
16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\
8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\
4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\
16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\
2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\
4 & 8 & 16 & 8 & 4 & 16 & 2 & 1
\end{array}\right)\)
