Elliptic curves in class 8.3-b over 4.4.9248.1
Isogeny class 8.3-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 8.3-b1
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} + 10 a^{2} - 7 a - 21\) , \( 9 a^{3} + 6 a^{2} - 21 a + 15\bigr] \)
|
| 8.3-b2
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} - 7 a + 24\) , \( -a^{3} - 14 a^{2} + 24 a + 105\bigr] \)
|
| 8.3-b3
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( -13 a^{3} - 41 a^{2} - 21 a - 2\) , \( -224 a^{3} - 527 a^{2} + 2 a + 165\bigr] \)
|
| 8.3-b4
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - a - 2\) , \( -3 a^{3} - 14 a^{2} + 3\bigr] \)
|
| 8.3-b5
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - a - 2\) , \( 2 a^{3} + 5 a^{2} - 3\bigr] \)
|
| 8.3-b6
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 17 a^{3} - 41 a^{2} + 19 a - 2\) , \( 138 a^{3} - 337 a^{2} - 2 a + 105\bigr] \)
|
| 8.3-b7
| \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + 3 a^{2} + 3 a + 3\) , \( 2 a^{3} + 7 a^{2} + 4 a - 4\bigr] \)
|
| 8.3-b8
| \( \bigl[a^{3} - 4 a\) , \( -1\) , \( a^{3} - 4 a\) , \( -3\) , \( 6 a^{2} - 4\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 2 & 8 & 4 & 2 & 8 & 4 & 2 \\
2 & 1 & 16 & 8 & 4 & 16 & 8 & 4 \\
8 & 16 & 1 & 2 & 4 & 4 & 8 & 16 \\
4 & 8 & 2 & 1 & 2 & 2 & 4 & 8 \\
2 & 4 & 4 & 2 & 1 & 4 & 2 & 4 \\
8 & 16 & 4 & 2 & 4 & 1 & 8 & 16 \\
4 & 8 & 8 & 4 & 2 & 8 & 1 & 8 \\
2 & 4 & 16 & 8 & 4 & 16 & 8 & 1
\end{array}\right)\)
