Elliptic curves in class 5.1-a over 6.6.1241125.1
Isogeny class 5.1-a contains
4 curves linked by isogenies of
degrees dividing 15.
| Curve label |
Weierstrass Coefficients |
| 5.1-a1
| \( \bigl[a^{5} - 7 a^{3} - a^{2} + 12 a + 4\) , \( 3 a^{5} - 2 a^{4} - 20 a^{3} + 5 a^{2} + 30 a + 11\) , \( -3 a^{5} + 2 a^{4} + 20 a^{3} - 5 a^{2} - 30 a - 9\) , \( 23 a^{5} - 29 a^{4} - 127 a^{3} + 109 a^{2} + 123 a + 24\) , \( 95 a^{5} - 121 a^{4} - 514 a^{3} + 463 a^{2} + 467 a + 73\bigr] \)
|
| 5.1-a2
| \( \bigl[-2 a^{5} + a^{4} + 14 a^{3} - a^{2} - 22 a - 9\) , \( a^{3} + a^{2} - 4 a - 4\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 18 a - 6\) , \( -2 a^{5} + 4 a^{4} + 18 a^{3} - 10 a^{2} - 35 a - 11\) , \( a^{5} + 4 a^{4} + a^{3} - 12 a^{2} - 11 a - 3\bigr] \)
|
| 5.1-a3
| \( \bigl[-5 a^{5} + 2 a^{4} + 34 a^{3} - 2 a^{2} - 52 a - 19\) , \( -2 a^{5} + 13 a^{3} + 3 a^{2} - 19 a - 7\) , \( a^{2} + a - 2\) , \( 20 a^{5} - 9 a^{4} - 145 a^{3} + 8 a^{2} + 244 a + 98\) , \( 13 a^{5} - 7 a^{4} - 106 a^{3} - 6 a^{2} + 200 a + 114\bigr] \)
|
| 5.1-a4
| \( \bigl[-4 a^{5} + 2 a^{4} + 27 a^{3} - 3 a^{2} - 42 a - 15\) , \( 5 a^{5} - 2 a^{4} - 34 a^{3} + 3 a^{2} + 53 a + 15\) , \( -3 a^{5} + a^{4} + 20 a^{3} - 30 a - 12\) , \( 12 a^{5} - 2 a^{4} - 86 a^{3} - 12 a^{2} + 146 a + 71\) , \( 80 a^{5} + 15 a^{4} - 507 a^{3} - 179 a^{2} + 627 a + 273\bigr] \)
|
Rank: \( 0 \)
\(\left(\begin{array}{rrrr}
1 & 15 & 3 & 5 \\
15 & 1 & 5 & 3 \\
3 & 5 & 1 & 15 \\
5 & 3 & 15 & 1
\end{array}\right)\)
