Elliptic curves in class 252.1-h over \(\Q(\sqrt{7}) \)
Isogeny class 252.1-h contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 252.1-h1
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -113\) , \( 516\bigr] \)
|
| 252.1-h2
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 7\) , \( 0\bigr] \)
|
| 252.1-h3
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 341 a - 897\) , \( -2000 a + 5296\bigr] \)
|
| 252.1-h4
| \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -22113 a - 58533\) , \( 2783748 a + 7365183\bigr] \)
|
| 252.1-h5
| \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -3063 a - 8103\) , \( -155052 a - 410229\bigr] \)
|
| 252.1-h6
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 3066 a - 8107\) , \( 146945 a - 388776\bigr] \)
|
| 252.1-h7
| \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -21938 a - 58043\) , \( 2833763 a + 7497434\bigr] \)
|
| 252.1-h8
| \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 22116 a - 58537\) , \( -2842285 a + 7519986\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\
3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\
6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\
4 & 12 & 6 & 1 & 3 & 12 & 2 & 4 \\
12 & 4 & 2 & 3 & 1 & 4 & 6 & 12 \\
12 & 4 & 2 & 12 & 4 & 1 & 6 & 3 \\
2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\
4 & 12 & 6 & 4 & 12 & 3 & 2 & 1
\end{array}\right)\)
