Elliptic curves in class 25.1-a over 4.4.6809.1
Isogeny class 25.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 25.1-a1
| \( \bigl[a^{2} + a - 3\) , \( -a^{2} + a + 4\) , \( a^{3} - 4 a\) , \( 10 a^{3} - 4 a^{2} - 42 a + 13\) , \( -8 a^{3} - 16 a^{2} + 44 a + 101\bigr] \)
|
| 25.1-a2
| \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 3\) , \( -152 a^{3} + 75 a^{2} + 687 a - 243\) , \( 1318 a^{3} - 819 a^{2} - 6230 a + 2290\bigr] \)
|
| 25.1-a3
| \( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 6 a - 4\) , \( a^{2} + a - 3\) , \( -12 a^{3} + 5 a^{2} + 52 a - 13\) , \( 20 a^{3} - 12 a^{2} - 97 a + 30\bigr] \)
|
| 25.1-a4
| \( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{3} + a^{2} - 5 a - 3\) , \( 10 a^{3} - 21 a^{2} - 116 a - 58\) , \( -148 a^{3} - 141 a^{2} + 488 a + 303\bigr] \)
|
| 25.1-a5
| \( \bigl[1\) , \( a^{3} - 6 a - 1\) , \( a\) , \( 759 a^{3} + 65 a^{2} - 3337 a - 1817\) , \( -15980 a^{3} - 2917 a^{2} + 72910 a + 40314\bigr] \)
|
| 25.1-a6
| \( \bigl[1\) , \( -a^{3} + 5 a\) , \( a^{2} + a - 3\) , \( -a^{3} - 4 a^{2} - 3 a + 3\) , \( -7 a^{3} - 15 a^{2} - a\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 4 & 2 & 4 & 8 \\
8 & 1 & 2 & 4 & 8 & 4 \\
4 & 2 & 1 & 2 & 4 & 2 \\
2 & 4 & 2 & 1 & 2 & 4 \\
4 & 8 & 4 & 2 & 1 & 8 \\
8 & 4 & 2 & 4 & 8 & 1
\end{array}\right)\)
