Elliptic curves in class 7.1-a over 4.4.8069.1
Isogeny class 7.1-a contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 7.1-a1
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -30 a^{3} - 4 a^{2} + 123 a - 94\) , \( -3 a^{3} - 229 a^{2} - 167 a + 555\bigr] \)
|
| 7.1-a2
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -4 a^{2} + 8 a - 4\) , \( 8 a^{3} - 31 a^{2} + 13 a + 16\bigr] \)
|
| 7.1-a3
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( a^{2} - 2 a + 1\) , \( 0\bigr] \)
|
| 7.1-a4
| \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 0\) , \( -270 a^{3} - 239 a^{2} + 643 a + 1\) , \( -5079 a^{3} - 5988 a^{2} + 12552 a + 2883\bigr] \)
|
| 7.1-a5
| \( \bigl[a\) , \( a^{3} - 5 a\) , \( a^{3} - 3 a + 1\) , \( 205 a^{3} + 249 a^{2} - 971 a - 1165\) , \( 6904 a^{3} - 925 a^{2} - 32778 a + 6181\bigr] \)
|
| 7.1-a6
| \( \bigl[a\) , \( a^{3} - 5 a\) , \( a^{3} - 3 a + 1\) , \( 15 a^{3} + 4 a^{2} - 66 a - 15\) , \( 124 a^{3} + 24 a^{2} - 588 a - 100\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 4 & 2 & 2 & 4 \\
2 & 1 & 2 & 4 & 4 & 2 \\
4 & 2 & 1 & 8 & 8 & 4 \\
2 & 4 & 8 & 1 & 4 & 8 \\
2 & 4 & 8 & 4 & 1 & 8 \\
4 & 2 & 4 & 8 & 8 & 1
\end{array}\right)\)
