Elliptic curves in class 31.1-c over 4.4.4400.1
Isogeny class 31.1-c contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 31.1-c1
| \( \bigl[a^{2} + a - 4\) , \( -a^{3} - a^{2} + 4 a + 4\) , \( a^{3} - 4 a\) , \( -3 a^{2} + 12\) , \( -30 a^{3} + 64 a^{2} + 72 a - 153\bigr] \)
|
| 31.1-c2
| \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( a^{3} - 3 a + 1\) , \( 1705 a^{3} + 2619 a^{2} - 7917 a - 12187\) , \( -77155 a^{3} - 119042 a^{2} + 356436 a + 550022\bigr] \)
|
| 31.1-c3
| \( \bigl[a^{2} - 3\) , \( a^{3} - a^{2} - 5 a + 4\) , \( a\) , \( -207 a^{3} + 313 a^{2} + 973 a - 1484\) , \( -3221 a^{3} + 4986 a^{2} + 14820 a - 22909\bigr] \)
|
| 31.1-c4
| \( \bigl[a^{3} - 4 a\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -79 a^{3} - 151 a^{2} + 198 a + 339\) , \( 713 a^{3} + 1513 a^{2} - 1708 a - 3582\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 4 & 2 & 4 \\
4 & 1 & 2 & 4 \\
2 & 2 & 1 & 2 \\
4 & 4 & 2 & 1
\end{array}\right)\)
