Elliptic curves in class 3.1-b over 6.6.1387029.1
Isogeny class 3.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 3.1-b1
| \( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 3 a + 3\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + a - 5\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( 38 a^{5} - 79 a^{4} - 119 a^{3} + 224 a^{2} + 58 a - 100\) , \( -805 a^{5} + 2210 a^{4} + 2234 a^{3} - 6650 a^{2} - 1026 a + 2946\bigr] \)
|
| 3.1-b2
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 15 a^{2} + 5 a - 4\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 14 a^{2} - 7 a + 4\) , \( -19 a^{5} + 51 a^{4} + 48 a^{3} - 155 a^{2} - 15 a + 74\) , \( 558 a^{5} - 1511 a^{4} - 1534 a^{3} + 4570 a^{2} + 700 a - 2027\bigr] \)
|
| 3.1-b3
| \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 3 a - 2\) , \( 2 a^{5} - 5 a^{4} - 7 a^{3} + 15 a^{2} + 5 a - 4\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 14 a^{2} - 7 a + 4\) , \( 41 a^{5} - 109 a^{4} - 117 a^{3} + 330 a^{2} + 60 a - 141\) , \( 121 a^{5} - 332 a^{4} - 332 a^{3} + 1007 a^{2} + 150 a - 448\bigr] \)
|
| 3.1-b4
| \( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 3 a + 3\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + a - 5\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a\) , \( 73 a^{5} - 184 a^{4} - 204 a^{3} + 554 a^{2} + 93 a - 245\) , \( -405 a^{5} + 1156 a^{4} + 1102 a^{3} - 3506 a^{2} - 504 a + 1554\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 3 & 6 & 2 \\
3 & 1 & 2 & 6 \\
6 & 2 & 1 & 3 \\
2 & 6 & 3 & 1
\end{array}\right)\)
