Elliptic curves in class 21.1-b over 6.6.1387029.1
Isogeny class 21.1-b contains
6 curves linked by isogenies of
degrees dividing 8.
| Curve label |
Weierstrass Coefficients |
| 21.1-b1
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} + 8 a^{4} - 25 a^{3} - 36 a^{2} + 59 a - 18\) , \( -51 a^{4} + 102 a^{3} + 161 a^{2} - 213 a + 38\bigr] \)
|
| 21.1-b2
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 4 a - 3\) , \( a^{4} - 2 a^{3} - 1\bigr] \)
|
| 21.1-b3
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 4 a - 8\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 6 a - 2\bigr] \)
|
| 21.1-b4
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} + 48 a^{4} - 105 a^{3} - 151 a^{2} + 214 a - 133\) , \( 373 a^{4} - 746 a^{3} - 1290 a^{2} + 1662 a - 613\bigr] \)
|
| 21.1-b5
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} - 12 a^{4} + 15 a^{3} + 54 a^{2} - 51 a - 78\) , \( -39 a^{4} + 78 a^{3} + 163 a^{2} - 203 a - 226\bigr] \)
|
| 21.1-b6
| \( \bigl[a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{2} - a - 2\) , \( -2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{5} - 232 a^{4} + 455 a^{3} + 979 a^{2} - 1196 a - 1143\) , \( -3103 a^{4} + 6206 a^{3} + 13092 a^{2} - 16196 a - 15855\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrr}
1 & 4 & 2 & 8 & 4 & 8 \\
4 & 1 & 2 & 8 & 4 & 8 \\
2 & 2 & 1 & 4 & 2 & 4 \\
8 & 8 & 4 & 1 & 2 & 4 \\
4 & 4 & 2 & 2 & 1 & 2 \\
8 & 8 & 4 & 4 & 2 & 1
\end{array}\right)\)
