Elliptic curves in class 31.1-d over 4.4.4400.1
Isogeny class 31.1-d contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 31.1-d1
| \( \bigl[a^{3} + a^{2} - 4 a - 4\) , \( a^{3} - 5 a + 1\) , \( a\) , \( a^{3} - 3 a^{2} - 5 a + 13\) , \( -6 a^{3} + 14 a^{2} + 12 a - 32\bigr] \)
|
| 31.1-d2
| \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{2} + a - 5\) , \( a^{2} + a - 3\) , \( 607 a^{3} + 903 a^{2} - 2920 a - 4421\) , \( 18357 a^{3} + 28564 a^{2} - 83921 a - 130076\bigr] \)
|
| 31.1-d3
| \( \bigl[a^{2} - 3\) , \( a^{3} - 3 a\) , \( a^{3} - 4 a + 1\) , \( -41 a^{3} - 33 a^{2} + 126 a + 19\) , \( 73 a^{3} + 375 a^{2} - 47 a - 1109\bigr] \)
|
| 31.1-d4
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 5\) , \( a^{2} - 3\) , \( -61 a^{3} + 81 a^{2} + 328 a - 475\) , \( 651 a^{3} - 942 a^{2} - 3238 a + 4848\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 4 & 2 \\
4 & 1 & 4 & 2 \\
4 & 4 & 1 & 2 \\
2 & 2 & 2 & 1
\end{array}\right)\)
