Elliptic curves in class 3.1-a over 4.4.13768.1
Isogeny class 3.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 3.1-a1
| \( \bigl[a^{2} - 3\) , \( 1\) , \( a\) , \( -142 a^{3} + 211 a^{2} + 607 a - 578\) , \( 1290 a^{3} - 1921 a^{2} - 5510 a + 5275\bigr] \)
|
| 3.1-a2
| \( \bigl[a^{2} - 3\) , \( 1\) , \( a\) , \( 163 a^{3} - 244 a^{2} - 693 a + 667\) , \( 6877 a^{3} - 10242 a^{2} - 29371 a + 28118\bigr] \)
|
| 3.1-a3
| \( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 2 a^{2} + 4 a - 3\) , \( a^{3} - 4 a - 2\) , \( -7 a^{3} + 20 a^{2} - 2 a - 5\) , \( 9 a^{3} - 28 a^{2} + 9 a + 12\bigr] \)
|
| 3.1-a4
| \( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{2} - a - 2\) , \( -5 a^{2} - 10 a - 2\) , \( -9 a^{3} - 14 a^{2} + 11 a + 7\bigr] \)
|
| 3.1-a5
| \( \bigl[a^{3} - 5 a - 1\) , \( -a^{3} + 6 a + 1\) , \( a^{2} - a - 2\) , \( -5 a^{3} + 25 a + 13\) , \( -6 a^{3} + 31 a + 14\bigr] \)
|
| 3.1-a6
| \( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( -a^{3} + a^{2} + 3 a + 2\) , \( 4 a^{3} - a^{2} - 20 a - 9\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 4 & 2 & 2 \\
2 & 1 & 8 & 8 & 4 & 4 \\
4 & 8 & 1 & 4 & 2 & 8 \\
4 & 8 & 4 & 1 & 2 & 8 \\
2 & 4 & 2 & 2 & 1 & 4 \\
2 & 4 & 8 & 8 & 4 & 1
\end{array}\right)\)
