Elliptic curves in class 7.1-d over 6.6.1279733.1
Isogeny class 7.1-d contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 7.1-d1
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 6 a^{3} - 6 a^{2} - 19 a + 16\) , \( 2 a^{5} + 5 a^{4} - 13 a^{3} - 24 a^{2} + 14 a + 14\bigr] \)
|
| 7.1-d2
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 6 a^{3} - 6 a^{2} - 19 a + 11\) , \( a^{5} - 2 a^{3} - 4 a^{2} - 5 a + 5\bigr] \)
|
| 7.1-d3
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -205 a^{5} + 445 a^{4} + 901 a^{3} - 1561 a^{2} - 1329 a - 94\) , \( -3408 a^{5} + 5120 a^{4} + 17678 a^{3} - 17421 a^{2} - 27884 a - 2251\bigr] \)
|
| 7.1-d4
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( 5 a^{5} - 49 a^{3} + 19 a^{2} + 101 a - 59\) , \( 2 a^{5} - 47 a^{4} + 97 a^{3} + 113 a^{2} - 290 a + 88\bigr] \)
|
| 7.1-d5
| \( \bigl[a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 12 a^{2} - a + 6\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -5 a^{5} + 61 a^{3} - 31 a^{2} - 139 a + 1\) , \( -44 a^{5} - 33 a^{4} + 383 a^{3} + 59 a^{2} - 696 a - 54\bigr] \)
|
| 7.1-d6
| \( \bigl[a^{5} - a^{4} - 3 a^{3} + a^{2} + 1\) , \( -a^{3} + 4 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -47 a^{5} - 2 a^{4} + 213 a^{3} + 36 a^{2} - 154 a - 15\) , \( -1023 a^{5} + 4977 a^{3} + 800 a^{2} - 4246 a + 90\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 2 & 8 & 4 & 4 & 8 \\
2 & 1 & 4 & 2 & 2 & 4 \\
8 & 4 & 1 & 8 & 2 & 4 \\
4 & 2 & 8 & 1 & 4 & 8 \\
4 & 2 & 2 & 4 & 1 & 2 \\
8 & 4 & 4 & 8 & 2 & 1
\end{array}\right)\)
