Elliptic curves in class 15.1-a over 5.5.65657.1
Isogeny class 15.1-a contains
4 curves linked by isogenies of
degrees dividing 4.
| Curve label |
Weierstrass Coefficients |
| 15.1-a1
| \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 9 a - 6\) , \( -2 a^{4} + 3 a^{3} + 8 a^{2} - 7 a - 5\) , \( -a^{4} + a^{3} + 5 a^{2} - 2 a - 4\) , \( -46 a^{4} + 109 a^{3} + 43 a^{2} - 117 a - 48\) , \( 463 a^{4} - 1139 a^{3} - 594 a^{2} + 1290 a + 662\bigr] \)
|
| 15.1-a2
| \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 10 a^{4} - 10 a^{3} - 40 a^{2} + 16 a + 5\) , \( -25 a^{4} + 18 a^{3} + 100 a^{2} - 13 a - 9\bigr] \)
|
| 15.1-a3
| \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( a\) , \( -a^{4} + a^{3} + 4 a^{2} - a - 1\bigr] \)
|
| 15.1-a4
| \( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( a^{2} - 2\) , \( 20 a^{4} - 20 a^{3} - 75 a^{2} + 26 a\) , \( 30 a^{4} - 29 a^{3} - 120 a^{2} + 39 a + 19\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 2 & 4 & 4 \\
2 & 1 & 2 & 2 \\
4 & 2 & 1 & 4 \\
4 & 2 & 4 & 1
\end{array}\right)\)
