Elliptic curves in class 31.1-d over 4.4.8789.1
Isogeny class 31.1-d contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 31.1-d1
| \( \bigl[a^{3} - a^{2} - 5 a - 2\) , \( -a - 1\) , \( 0\) , \( 48 a^{3} - 128 a^{2} - 76 a + 28\) , \( 46 a^{3} - 121 a^{2} - 73 a + 26\bigr] \)
|
| 31.1-d2
| \( \bigl[a^{3} - a^{2} - 5 a - 2\) , \( -a - 1\) , \( 0\) , \( 508 a^{3} - 1353 a^{2} - 821 a + 283\) , \( -12729 a^{3} + 33998 a^{2} + 19826 a - 7716\bigr] \)
|
| 31.1-d3
| \( \bigl[2 a^{3} - 3 a^{2} - 10 a\) , \( 2 a^{3} - 3 a^{2} - 10 a - 2\) , \( a^{3} - 2 a^{2} - 4 a + 1\) , \( -242 a^{3} + 404 a^{2} + 1171 a - 287\) , \( -3175 a^{3} + 5490 a^{2} + 15103 a - 4738\bigr] \)
|
| 31.1-d4
| \( \bigl[a^{3} - 2 a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 7 a - 2\) , \( a^{3} - a^{2} - 6 a - 1\) , \( a^{3} - 4 a^{2} - 7 a + 8\) , \( 8 a^{3} - 7 a^{2} - 31 a + 5\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 2 & 2 \\
2 & 1 & 4 & 4 \\
2 & 4 & 1 & 4 \\
2 & 4 & 4 & 1
\end{array}\right)\)
