Elliptic curves in class 8.4-a over 4.4.9248.1
Isogeny class 8.4-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 8.4-a1
| \( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -3 a^{2} - 2\) , \( 3 a^{2} - 3\bigr] \)
|
| 8.4-a2
| \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} - 4 a + 1\) , \( 3 a^{3} - 10 a + 8\) , \( -5 a^{3} - 4 a^{2} + 12 a - 5\bigr] \)
|
| 8.4-a3
| \( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -14 a^{3} + 27 a^{2} + 19 a - 18\) , \( -136 a^{3} + 290 a^{2} + 72 a - 137\bigr] \)
|
| 8.4-a4
| \( \bigl[a + 1\) , \( a^{2} - a - 2\) , \( a^{2} - 3\) , \( -7 a^{3} - 13 a^{2} + 4 a + 7\) , \( 16 a^{3} + 35 a^{2} - 7 a - 17\bigr] \)
|
| 8.4-a5
| \( \bigl[a + 1\) , \( -a^{3} + 5 a - 1\) , \( 0\) , \( -8 a^{3} + 5 a^{2} + 37 a - 22\) , \( 18 a^{3} - 12 a^{2} - 82 a + 55\bigr] \)
|
| 8.4-a6
| \( \bigl[a + 1\) , \( a^{3} - 3 a - 1\) , \( a^{2} + a - 2\) , \( 108 a^{3} + 71 a^{2} - 498 a - 330\) , \( -1110 a^{3} - 740 a^{2} + 5050 a + 3345\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 4 & 8 \\
8 & 1 & 8 & 4 & 2 & 4 \\
4 & 8 & 1 & 2 & 4 & 8 \\
2 & 4 & 2 & 1 & 2 & 4 \\
4 & 2 & 4 & 2 & 1 & 2 \\
8 & 4 & 8 & 4 & 2 & 1
\end{array}\right)\)
