Elliptic curves in class 256.1-b over \(\Q(\sqrt{17}) \)
Isogeny class 256.1-b contains
12 curves linked by isogenies of
degrees dividing 24.
| Curve label |
Weierstrass Coefficients |
| 256.1-b1
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -144 a + 360\) , \( -6784 a + 17392\bigr] \)
|
| 256.1-b2
| \( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a - 24\) , \( -256 a - 400\bigr] \)
|
| 256.1-b3
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 144 a + 216\) , \( 6784 a + 10608\bigr] \)
|
| 256.1-b4
| \( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a - 40\) , \( 256 a - 656\bigr] \)
|
| 256.1-b5
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( -16 a - 28\bigr] \)
|
| 256.1-b6
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 15697 a - 40284\) , \( -1536816 a + 3936512\bigr] \)
|
| 256.1-b7
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 977 a - 2524\) , \( -23856 a + 61184\bigr] \)
|
| 256.1-b8
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 44\) , \( 0\bigr] \)
|
| 256.1-b9
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -175 a - 348\) , \( 1936 a + 2788\bigr] \)
|
| 256.1-b10
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -975 a - 1548\) , \( 22880 a + 35780\bigr] \)
|
| 256.1-b11
| \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 177 a - 524\) , \( -2112 a + 5248\bigr] \)
|
| 256.1-b12
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15695 a - 24588\) , \( 1521120 a + 2375108\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrrrrrrrr}
1 & 24 & 8 & 3 & 6 & 8 & 4 & 12 & 12 & 2 & 24 & 4 \\
24 & 1 & 3 & 8 & 4 & 12 & 6 & 2 & 8 & 12 & 4 & 24 \\
8 & 3 & 1 & 24 & 12 & 4 & 2 & 6 & 24 & 4 & 12 & 8 \\
3 & 8 & 24 & 1 & 2 & 24 & 12 & 4 & 4 & 6 & 8 & 12 \\
6 & 4 & 12 & 2 & 1 & 12 & 6 & 2 & 2 & 3 & 4 & 6 \\
8 & 12 & 4 & 24 & 12 & 1 & 2 & 6 & 24 & 4 & 3 & 8 \\
4 & 6 & 2 & 12 & 6 & 2 & 1 & 3 & 12 & 2 & 6 & 4 \\
12 & 2 & 6 & 4 & 2 & 6 & 3 & 1 & 4 & 6 & 2 & 12 \\
12 & 8 & 24 & 4 & 2 & 24 & 12 & 4 & 1 & 6 & 8 & 3 \\
2 & 12 & 4 & 6 & 3 & 4 & 2 & 6 & 6 & 1 & 12 & 2 \\
24 & 4 & 12 & 8 & 4 & 3 & 6 & 2 & 8 & 12 & 1 & 24 \\
4 & 24 & 8 & 12 & 6 & 8 & 4 & 12 & 3 & 2 & 24 & 1
\end{array}\right)\)
