Elliptic curves in class 25.1-e over 4.4.6809.1
Isogeny class 25.1-e contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 25.1-e1
| \( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 5 a\) , \( -9 a^{3} + 22 a^{2} + 28 a - 74\) , \( -56 a^{3} - 102 a^{2} + 580 a - 120\bigr] \)
|
| 25.1-e2
| \( \bigl[a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - a^{2} - 4 a + 3\) , \( a^{3} - 5 a\) , \( 21 a^{3} - 8 a^{2} - 77 a - 34\) , \( a^{3} - 44 a^{2} + 75 a + 47\bigr] \)
|
| 25.1-e3
| \( \bigl[a^{2} + a - 3\) , \( -a^{3} + a^{2} + 5 a - 2\) , \( a^{3} - 4 a - 1\) , \( 3 a^{3} + 2 a^{2} - 10 a - 3\) , \( 2 a^{3} + 3 a^{2} - 4 a - 4\bigr] \)
|
| 25.1-e4
| \( \bigl[a^{3} - 5 a - 1\) , \( -a^{2} + 2\) , \( a^{3} + a^{2} - 5 a - 3\) , \( -161 a^{3} + 94 a^{2} + 751 a - 277\) , \( 750 a^{3} - 443 a^{2} - 3494 a + 1313\bigr] \)
|
| 25.1-e5
| \( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{2} - 2\) , \( -2 a^{3} - 2 a^{2} + a - 5\) , \( 317 a^{3} + 730 a^{2} + 86 a - 140\bigr] \)
|
| 25.1-e6
| \( \bigl[1\) , \( -a + 1\) , \( a^{3} + a^{2} - 5 a - 4\) , \( -9 a^{3} + 4 a^{2} + 41 a - 12\) , \( -22 a^{3} + 14 a^{2} + 103 a - 46\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 8 & 4 & 4 \\
2 & 1 & 4 & 4 & 2 & 2 \\
8 & 4 & 1 & 4 & 8 & 2 \\
8 & 4 & 4 & 1 & 8 & 2 \\
4 & 2 & 8 & 8 & 1 & 4 \\
4 & 2 & 2 & 2 & 4 & 1
\end{array}\right)\)
