Elliptic curves in class 17.1-b over 4.4.14272.1
Isogeny class 17.1-b contains
4 curves linked by isogenies of
degrees dividing 6.
| Curve label |
Weierstrass Coefficients |
| 17.1-b1
| \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -848 a^{3} + 2260 a^{2} + 2564 a - 3510\) , \( -22808 a^{3} + 61558 a^{2} + 69436 a - 95032\bigr] \)
|
| 17.1-b2
| \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -48 a^{3} + 130 a^{2} + 144 a - 215\) , \( -466 a^{3} + 1261 a^{2} + 1414 a - 1971\bigr] \)
|
| 17.1-b3
| \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( -8 a^{3} + 20 a^{2} + 24 a - 35\) , \( -54 a^{3} + 149 a^{2} + 166 a - 231\bigr] \)
|
| 17.1-b4
| \( \bigl[2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 0\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 5\) , \( 2 a^{3} - 5 a^{2} - 6 a + 6\bigr] \)
|
Rank: \( 1 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 3 & 6 \\
2 & 1 & 6 & 3 \\
3 & 6 & 1 & 2 \\
6 & 3 & 2 & 1
\end{array}\right)\)
