Elliptic curves in class 5.1-b over 4.4.13676.1
Isogeny class 5.1-b contains
8 curves linked by isogenies of
degrees dividing 16.
| Curve label |
Weierstrass Coefficients |
| 5.1-b1
| \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 6 a - 5\) , \( a^{2} - 2\) , \( 109 a^{3} + 45 a^{2} - 590 a - 71\) , \( -689 a^{3} - 295 a^{2} + 3711 a + 477\bigr] \)
|
| 5.1-b2
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{2} - 3\) , \( a^{2} + a - 2\) , \( 48 a^{3} + 34 a^{2} - 224 a - 27\) , \( 170 a^{3} + 92 a^{2} - 867 a - 115\bigr] \)
|
| 5.1-b3
| \( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a\) , \( -28 a^{3} + 43 a^{2} + 178 a - 259\) , \( -202 a^{3} + 242 a^{2} + 1199 a - 1619\bigr] \)
|
| 5.1-b4
| \( \bigl[a\) , \( a^{3} - 5 a + 2\) , \( 0\) , \( -15 a^{3} - 15 a^{2} + 54 a - 3\) , \( 47 a^{3} + 54 a^{2} - 162 a - 15\bigr] \)
|
| 5.1-b5
| \( \bigl[a\) , \( -a^{3} - a^{2} + 4 a + 2\) , \( a^{3} - 5 a + 2\) , \( -61 a^{3} - 16 a^{2} + 330 a - 16\) , \( -517 a^{3} - 336 a^{2} + 2754 a + 989\bigr] \)
|
| 5.1-b6
| \( \bigl[1\) , \( -a^{3} + 5 a - 1\) , \( a^{2} - 2\) , \( -212 a^{3} - 275 a^{2} + 756 a + 102\) , \( -3442 a^{3} - 4269 a^{2} + 12008 a + 1611\bigr] \)
|
| 5.1-b7
| \( \bigl[a^{3} - 5 a + 3\) , \( a\) , \( a^{3} - 5 a + 3\) , \( -a^{2} + 6 a - 7\) , \( -a^{2} + 5 a - 6\bigr] \)
|
| 5.1-b8
| \( \bigl[a^{3} - 5 a + 3\) , \( a\) , \( a^{3} - 5 a + 3\) , \( 4 a^{2} - 14 a + 13\) , \( 11 a^{3} - 32 a^{2} + 8 a + 21\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrrrrrr}
1 & 8 & 4 & 2 & 2 & 8 & 2 & 4 \\
8 & 1 & 2 & 16 & 16 & 4 & 4 & 8 \\
4 & 2 & 1 & 8 & 8 & 2 & 2 & 4 \\
2 & 16 & 8 & 1 & 4 & 16 & 4 & 8 \\
2 & 16 & 8 & 4 & 1 & 16 & 4 & 8 \\
8 & 4 & 2 & 16 & 16 & 1 & 4 & 8 \\
2 & 4 & 2 & 4 & 4 & 4 & 1 & 2 \\
4 & 8 & 4 & 8 & 8 & 8 & 2 & 1
\end{array}\right)\)
