Elliptic curves in class 512.3-g over 4.4.2777.1
Isogeny class 512.3-g contains
4 curves linked by isogenies of
degrees dividing 14.
| Curve label |
Weierstrass Coefficients |
| 512.3-g1
| \( \bigl[a^{2} - a - 2\) , \( -a^{3} + 2 a^{2} + 3 a - 4\) , \( a\) , \( -a^{3} - 7 a^{2} - 4 a + 8\) , \( -10 a^{3} - 10 a^{2} + 10 a + 3\bigr] \)
|
| 512.3-g2
| \( \bigl[a^{3} - 4 a\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( 0\) , \( -756 a^{3} + 2036 a^{2} + 1496 a - 4993\) , \( -59611 a^{3} + 65161 a^{2} + 200305 a - 50787\bigr] \)
|
| 512.3-g3
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - a - 2\) , \( -7800 a^{3} + 13289 a^{2} + 21949 a - 24086\) , \( -559021 a^{3} + 935695 a^{2} + 1603430 a - 1630220\bigr] \)
|
| 512.3-g4
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{3} - 2 a^{2} - 2 a + 4\) , \( a^{2} - a - 2\) , \( 10 a^{3} - a^{2} - 41 a - 26\) , \( 27 a^{3} + 7 a^{2} - 122 a - 108\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 7 & 14 & 2 \\
7 & 1 & 2 & 14 \\
14 & 2 & 1 & 7 \\
2 & 14 & 7 & 1
\end{array}\right)\)
