Elliptic curves in class 31.2-a over 4.4.725.1
Isogeny class 31.2-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 31.2-a1
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -115 a^{3} + 395 a^{2} + 120 a - 934\) , \( -1763 a^{3} + 4933 a^{2} + 2430 a - 10526\bigr] \)
|
| 31.2-a2
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 5 a^{3} - 5 a^{2} + 10 a - 49\) , \( 26 a^{3} - 50 a^{2} + 56 a - 129\bigr] \)
|
| 31.2-a3
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -5 a^{3} + 5 a^{2} - 10 a - 39\) , \( 20 a^{3} + 4 a^{2} + 36 a + 83\bigr] \)
|
| 31.2-a4
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( -4\) , \( a^{3} - a^{2} + 2 a - 1\bigr] \)
|
| 31.2-a5
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
|
| 31.2-a6
| \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{3} + a^{2} + a - 1\) , \( 0\) , \( 205 a^{3} - 485 a^{2} + 60 a + 116\) , \( 3195 a^{3} - 7469 a^{2} + 618 a + 2116\bigr] \)
|
Rank not yet determined.
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 8 & 4 \\
2 & 1 & 4 & 2 & 4 & 2 \\
8 & 4 & 1 & 2 & 4 & 8 \\
4 & 2 & 2 & 1 & 2 & 4 \\
8 & 4 & 4 & 2 & 1 & 8 \\
4 & 2 & 8 & 4 & 8 & 1
\end{array}\right)\)
