Elliptic curves in class 31.1-a over 4.4.1957.1
Isogeny class 31.1-a contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 31.1-a1
| \( \bigl[0\) , \( a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( 69 a^{3} + 29 a^{2} - 257 a - 177\) , \( 387 a^{3} + 140 a^{2} - 1515 a - 1004\bigr] \)
|
| 31.1-a2
| \( \bigl[0\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 4 a\) , \( 2 a^{3} + 2 a^{2} - 8 a - 6\) , \( -5 a^{3} - 2 a^{2} + 18 a + 11\bigr] \)
|
| 31.1-a3
| \( \bigl[0\) , \( a^{3} - 5 a\) , \( -a^{3} + a^{2} + 4 a\) , \( -28 a^{3} - 38 a^{2} + 52 a + 54\) , \( -103 a^{3} - 116 a^{2} + 64 a - 103\bigr] \)
|
| 31.1-a4
| \( \bigl[0\) , \( -a^{3} + 3 a\) , \( 1\) , \( 3 a^{3} - 2 a^{2} - 10 a + 5\) , \( -2 a^{3} + a^{2} + 7 a - 2\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 15 & 3 & 5 \\
15 & 1 & 5 & 3 \\
3 & 5 & 1 & 15 \\
5 & 3 & 15 & 1
\end{array}\right)\)
