Elliptic curves in class 57600.1-p over \(\Q(\sqrt{-3}) \)
Isogeny class 57600.1-p contains
8 curves linked by isogenies of
degrees dividing 12.
| Curve label |
Weierstrass Coefficients |
| 57600.1-p1
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -648 a\) , \( -24480 a + 12240\bigr] \)
|
| 57600.1-p2
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 72 a\) , \( 864 a - 432\bigr] \)
|
| 57600.1-p3
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -21768 a\) , \( -208800 a + 104400\bigr] \)
|
| 57600.1-p4
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -3288 a\) , \( -74400 a + 37200\bigr] \)
|
| 57600.1-p5
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -888 a\) , \( 10080 a - 5040\bigr] \)
|
| 57600.1-p6
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -16008 a\) , \( -909216 a + 454608\bigr] \)
|
| 57600.1-p7
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -13848 a\) , \( 715104 a - 357552\bigr] \)
|
| 57600.1-p8
| \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -256008 a\) , \( -57741216 a + 28870608\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\
3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\
4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\
12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\
6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\
2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\
12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\
4 & 12 & 4 & 3 & 6 & 2 & 12 & 1
\end{array}\right)\)
