Elliptic curves in class 17.1-b over 4.4.7168.1
Isogeny class 17.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 17.1-b1
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 3 a^{3} + 4 a^{2} - 11 a - 13\) , \( 3 a^{3} + 4 a^{2} - 12 a - 15\bigr] \)
|
| 17.1-b2
| \( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{2} - 2\) , \( 0\) , \( 0\bigr] \)
|
| 17.1-b3
| \( \bigl[a^{3} - 3 a\) , \( a - 1\) , \( a^{2} - 2\) , \( 5 a^{3} - 20 a^{2} + 25 a - 10\) , \( 51 a^{3} - 139 a^{2} + 21 a + 92\bigr] \)
|
| 17.1-b4
| \( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 3 a - 2\) , \( 123 a^{3} + 154 a^{2} - 546 a - 688\) , \( 1438 a^{3} + 1804 a^{2} - 6375 a - 8022\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 6 & 3 \\
2 & 1 & 3 & 6 \\
6 & 3 & 1 & 2 \\
3 & 6 & 2 & 1
\end{array}\right)\)
