Elliptic curves in class 704.3-r over 4.4.2777.1
Isogeny class 704.3-r contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 704.3-r1
| \( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 3\) , \( a^{3} - 4 a\) , \( -22 a^{3} + 30 a^{2} + 63 a - 67\) , \( 61 a^{3} - 115 a^{2} - 201 a + 209\bigr] \)
|
| 704.3-r2
| \( \bigl[a^{2} - 2\) , \( a^{3} - 3 a - 2\) , \( a^{3} - 4 a\) , \( 3 a^{3} - 4 a^{2} - 7 a + 9\) , \( 9 a^{3} - 13 a^{2} - 25 a + 21\bigr] \)
|
| 704.3-r3
| \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 4 a\) , \( 0\) , \( 9 a^{3} - 7 a^{2} - 19 a - 19\) , \( -18 a^{3} + 25 a^{2} + 37 a + 17\bigr] \)
|
| 704.3-r4
| \( \bigl[a^{3} - 3 a\) , \( a^{3} - a^{2} - 4 a\) , \( 0\) , \( 49 a^{3} - 192 a^{2} + 101 a + 161\) , \( -755 a^{3} + 1819 a^{2} + 217 a - 919\bigr] \)
|
| 704.3-r5
| \( \bigl[a\) , \( -a^{3} + 3 a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -486 a^{3} + 840 a^{2} + 1369 a - 1515\) , \( -7344 a^{3} + 12462 a^{2} + 20884 a - 22065\bigr] \)
|
| 704.3-r6
| \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( 0\) , \( 3 a^{3} - 5 a^{2} - 6 a - 1\) , \( a^{3} + 4 a^{2} - 14 a - 11\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrrrr}
1 & 8 & 2 & 4 & 8 & 4 \\
8 & 1 & 4 & 8 & 4 & 2 \\
2 & 4 & 1 & 2 & 4 & 2 \\
4 & 8 & 2 & 1 & 8 & 4 \\
8 & 4 & 4 & 8 & 1 & 2 \\
4 & 2 & 2 & 4 & 2 & 1
\end{array}\right)\)
