Elliptic curves in class 228.1-s over \(\Q(\sqrt{57}) \)
Isogeny class 228.1-s contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 228.1-s1
| \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5049692 a - 16537318\) , \( 13049407660 a + 42735729826\bigr] \)
|
| 228.1-s2
| \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 386308 a + 1265132\) , \( -19979150 a - 65430062\bigr] \)
|
| 228.1-s3
| \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -96892 a - 317308\) , \( -2306310 a - 7552974\bigr] \)
|
| 228.1-s4
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 29535 a - 126260\) , \( -5355845 a + 22895794\bigr] \)
|
| 228.1-s5
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -365 a - 1195\) , \( 7195 a + 23563\bigr] \)
|
| 228.1-s6
| \( \bigl[1\) , \( 1\) , \( 0\) , \( 365 a - 1560\) , \( -7195 a + 30758\bigr] \)
|
| 228.1-s7
| \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5170492 a - 16932928\) , \( 12440941710 a + 40743054210\bigr] \)
|
| 228.1-s8
| \( \bigl[1\) , \( 1\) , \( 0\) , \( -29535 a - 96725\) , \( 5355845 a + 17539949\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\
3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\
6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\
4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\
12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\
12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\
2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\
4 & 12 & 6 & 4 & 3 & 12 & 2 & 1
\end{array}\right)\)
