Elliptic curves in class 47.1-a over 6.6.1541581.1
Isogeny class 47.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 47.1-a1
| \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 5 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( -28 a^{4} - 14 a^{3} + 71 a^{2} + 35 a - 11\) , \( -102 a^{5} - 88 a^{4} + 262 a^{3} + 214 a^{2} - 40 a - 15\bigr] \)
|
| 47.1-a2
| \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 10 a^{2} + 5 a - 1\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( 5 a^{5} - 13 a^{4} - 19 a^{3} + 36 a^{2} + 20 a - 11\) , \( -19 a^{5} + 34 a^{4} + 71 a^{3} - 91 a^{2} - 60 a + 19\bigr] \)
|
| 47.1-a3
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} - a + 4\) , \( a + 1\) , \( -3 a^{5} + 3 a^{4} + 18 a^{3} - 3 a^{2} - 30 a - 11\) , \( 2 a^{5} - 14 a^{3} - 5 a^{2} + 18 a + 8\bigr] \)
|
| 47.1-a4
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 13 a^{2} - a + 4\) , \( a + 1\) , \( -108 a^{5} + 78 a^{4} + 683 a^{3} - 33 a^{2} - 1030 a - 441\) , \( -1436 a^{5} + 1098 a^{4} + 8849 a^{3} - 648 a^{2} - 13035 a - 4987\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
